diff --git a/Moody_pipeline.ipynb b/Moody_pipeline.ipynb new file mode 100644 index 0000000..5e324e9 --- /dev/null +++ b/Moody_pipeline.ipynb @@ -0,0 +1,5834 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "cFAMXPSwxjvI", + "outputId": "196423b5-522e-480c-f469-cf05ec2c0fdf" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "fatal: destination path '2025-Moodys' already exists and is not an empty directory.\n", + "Requirement already satisfied: giotto-tda in 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"ugOpPkrRlorV" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "\n", + "time_series = np.log(pd.read_csv(r\"/content/2025-Moodys/sp500.csv\", header=None).to_numpy().squeeze())" + ], + "metadata": { + "id": "bsvOLdZ1x1m8" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "\n", + "def takens_embedding(time_series, N, d):\n", + "\n", + " L = len(time_series)\n", + " Z = []\n", + "\n", + " for t in range(L - (N - 1) * d):\n", + " z_t = [time_series[t + i * d] for i in range(N)]\n", + " Z.append(z_t)\n", + "\n", + " return np.array(Z)\n", + "\n", + "def sliding_window(point_cloud, w):\n", + "\n", + " K = len(point_cloud) - w + 1\n", + " windows = []\n", + "\n", + " for t in range(K):\n", + " Z_t = point_cloud[t:t + w]\n", + " windows.append(Z_t)\n", + "\n", + " return windows\n", + "\n", + "\n", + "\n", + "\n", + "def generate_boundary_operator(simplex_tree, k):\n", + " \"\"\"\n", + " Generates the boundary operator matrix ∂_k for a simplicial complex represented by a simplex tree.\n", + "\n", + " Args:\n", + " simplex_tree: A simplex tree data structure containing ordered simplices.\n", + " k (int): The dimension of the simplices for which to compute the boundary operator.\n", + "\n", + " Returns:\n", + " np.ndarray: A sparse matrix where entry [i][j] is the coefficient of the (k-1)-simplex i\n", + " in the boundary of the k-simplex j.\n", + " \"\"\"\n", + " # Edge case: boundary of 0-simplices is trivial\n", + " if k == 0:\n", + " return np.zeros((0, len(simplex_tree[k]))) # Empty matrix\n", + "\n", + " # Extract ordered lists of k-simplices and (k-1)-simplices\n", + " k_simplices = simplex_tree[k] # Columns of the matrix\n", + " km1_simplices = simplex_tree[k-1] # Rows of the matrix\n", + "\n", + " # Create a dictionary to map (k-1)-simplices to their row indices\n", + " km1_simplex_to_index = {tuple(s): idx for idx, s in enumerate(km1_simplices)}\n", + "\n", + " # Initialize the boundary matrix with zeros\n", + " boundary_matrix = np.zeros((len(km1_simplices), len(k_simplices)), dtype=int)\n", + "\n", + " # Iterate over each k-simplex (column j)\n", + " for j, s_k in enumerate(k_simplices):\n", + " # Remove each vertex at position t and compute the boundary\n", + " for t in range(len(s_k)):\n", + " # Generate the (k-1)-simplex by removing vertex t\n", + " s_km1 = tuple(s_k[:t] + s_k[t+1:])\n", + "\n", + " # Get the row index for this (k-1)-simplex\n", + " if s_km1 in km1_simplex_to_index:\n", + " i = km1_simplex_to_index[s_km1]\n", + " # Assign coefficient (-1)^t to matrix entry [i][j]\n", + " boundary_matrix[i][j] = (-1) ** t\n", + "\n", + " return boundary_matrix\n", + "\n", + "def generate_k_laplasian_matrix(grouped_simplices_per_filtration,k,i_simplice):\n", + " simplextree_zero = grouped_simplices_per_filtration[i_simplice]\n", + " boundary_1=generate_boundary_operator(simplextree_zero, k)\n", + " partial_1=np.dot(boundary_1.T,boundary_1)\n", + " if len(simplextree_zero)==2:\n", + " return partial_1\n", + " boundary_2=generate_boundary_operator(simplextree_zero, k+1)\n", + " partial_2=np.dot(boundary_2,boundary_2.T)\n", + " delta1=partial_1+partial_2\n", + " return delta1\n", + "\n", + "def is_power_of_two(n):\n", + " \"\"\"Check if n is a power of two.\"\"\"\n", + " return n != 0 and (n & (n - 1)) == 0\n", + "\n", + "def next_power_of_two(n):\n", + " \"\"\"Find the smallest power of two greater than or equal to n.\"\"\"\n", + " if n == 0:\n", + " return 1\n", + " return 1 << (n - 1).bit_length()\n", + "\n", + "def pad_matrix_to_power_of_two(matrix):\n", + "\n", + " n = len(matrix)\n", + " # Validate the matrix is square\n", + " for row in matrix:\n", + " if len(row) != n:\n", + " raise ValueError(\"Matrix must be square.\")\n", + "\n", + " # Calculate the next power of two and its exponent k\n", + " m = next_power_of_two(n)\n", + " k = m.bit_length() - 1 # Since m is 2^k\n", + "\n", + " # Create a new matrix filled with zeros\n", + " padded_matrix = [[0] * m for _ in range(m)]\n", + "\n", + " # Copy the original matrix into the top-left corner\n", + " for i in range(n):\n", + " for j in range(n):\n", + " padded_matrix[i][j] = matrix[i][j]\n", + "\n", + " # Fill the new diagonal elements with k\n", + " for i in range(n, m):\n", + " padded_matrix[i][i] = k\n", + "\n", + " return padded_matrix\n", + "\n", + "\n" + ], + "metadata": { + "id": "gbPIe2CYx3O2" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "#step 1\n", + "def generate_point_cloud(time_series, N, d, w):\n", + "\n", + " Z = takens_embedding(time_series, N, d)\n", + " point_cloud = sliding_window(Z, w)\n", + "\n", + " return point_cloud\n", + "\n", + "\n", + "\n" + ], + "metadata": { + "id": "RD-tUN694qLu" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + " #step 2\n", + "def bitstring_to_phase(bitstring):\n", + " return int(bitstring, 2) / (2 ** len(bitstring))\n", + "def generate_simplex_groups(point_cloud,epsilon):\n", + " grouped_simplices_per_filtration = []\n", + "\n", + " for cloud in point_cloud:\n", + " rips_complex = gudhi.RipsComplex(points=cloud, max_edge_length=epsilon)\n", + " simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)\n", + "\n", + " filtration = simplex_tree.get_filtration()\n", + " grouped_simplices = {}\n", + "\n", + " for simplex, _ in filtration:\n", + " dim = len(simplex) - 1 # Dimension of the simplex\n", + " if dim not in grouped_simplices:\n", + " grouped_simplices[dim] = []\n", + " grouped_simplices[dim].append(simplex)\n", + "\n", + " # Convert dictionary to sorted list of lists (by dimension)\n", + " grouped_simplices_per_filtration.append([grouped_simplices[dim] for dim in sorted(grouped_simplices.keys())])\n", + "\n", + " # Output the list of lists for each filtration\n", + " # for idx, filtration in enumerate(grouped_simplices_per_filtration):\n", + " # print(f\"Filtration {idx}: {filtration}\")\n", + " return grouped_simplices_per_filtration\n", + "import math\n", + "def generate_U(grouped_simplices_per_filtration):\n", + " betty_value_per_cloud=[]\n", + " for i in range(len(grouped_simplices_per_filtration)):\n", + " delta=generate_k_laplasian_matrix(grouped_simplices_per_filtration,1,i)\n", + " H=np.array(pad_matrix_to_power_of_two(delta))\n", + " iH = 1j * H\n", + " U = expm(iH)\n", + " number_of_target_qubits = int(math.log2(U.shape[0]))\n", + " print(U.shape)\n", + " mixed_state_circuit = mixed_state_preparation(number_of_target_qubits)\n", + " print('8'*10000)\n", + " qpe_circuit = quantum_phase_estimation(mixed_state_circuit, number_of_target_qubits,U)\n", + " circ = transpile(qpe_circuit, simulator)\n", + " result = simulator.run(circ).result()\n", + " counts = result.get_counts(circ)\n", + "\n", + "\n", + " # Convert the bitstrings from the result\n", + " phase_estimates = [bitstring_to_phase(bitstring) for bitstring in result.get_counts().keys()]\n", + " alpha = sum(counts.values())\n", + "\n", + " # Count occurrences of '000' in the first three qubits\n", + " zero_state_count = sum(v for k, v in counts.items() if k[:3] == '000')\n", + "\n", + " # Compute probability p(0)\n", + " p_0 = zero_state_count / alpha\n", + " print(f\"p(0) = {p_0:.4f}\")\n", + "\n", + "\n", + " q = 3 # Number of qubits for phase estimation\n", + " beta_k_tilde = (2**q) * p_0\n", + " print(f\"Estimated Betti Number: {beta_k_tilde:.4f}\")\n", + " betty_value_per_cloud.append(beta_k_tilde)\n", + "\n", + " return betty_value_per_cloud" + ], + "metadata": { + "id": "sCsEt3t_4un1" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "70bOxzI7ogRY" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit.library import QFT\n", + "from qiskit.circuit.library import UnitaryGate\n", + "import numpy as np\n", + "\n", + "\n", + "def mixed_state_preparation(number_of_target_qubits):\n", + " num_qubits = number_of_target_qubits*3\n", + " qc = QuantumCircuit(num_qubits, num_qubits, name=\"Custom Circuit\")\n", + "\n", + " # Prepare entangled state between qubits 3-5 and 6-8\n", + " for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + " qc.h(i)\n", + "\n", + " output = []\n", + " for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + " qc.cx(i, i+3)\n", + " output.append(i+number_of_target_qubits)\n", + "\n", + " # Measure auxiliary qubits (3-5)\n", + " print(output)\n", + " qc.measure(output, output)\n", + "\n", + " return qc\n", + "\n", + "def quantum_phase_estimation(qc, U_i ,number_of_target_qubits):\n", + " U_gate = UnitaryGate(U_i, label=\"U\")\n", + "\n", + " # Apply Hadamard to precision qubits (0-2)\n", + " for i in range(number_of_target_qubits):\n", + " qc.h(i)\n", + "\n", + " count_bits = []\n", + " unary = []\n", + "\n", + " for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + " unary.append(i)\n", + "\n", + " # Apply controlled-U^(2^j) operations\n", + " for j in range(number_of_target_qubits-1,-1,-1):\n", + " print(j)\n", + " power = 2 ** j\n", + " count_bits.append(j)\n", + " controlled_U = U_gate.power(power).control(1)\n", + "\n", + " qc.append(controlled_U, [number_of_target_qubits-j-1]+unary) # Control qubit j, targets 6-8\n", + "\n", + " # Apply inverse QFT on precision qubits\n", + " qft_inv = QFT(number_of_target_qubits, do_swaps=False).inverse()\n", + " qc.append(qft_inv, count_bits)\n", + "\n", + " # Measure precision qubits\n", + " qc.measure(count_bits, count_bits)\n", + "\n", + " return qc\n", + "\n", + "\n" + ], + "metadata": { + "id": "MIBCNZzunJO4" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "!pip install qiskit_aer" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "WLtZmeRxp81B", + "outputId": "e9f45430-ae71-4e27-9061-8c088e41f12b" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Requirement already satisfied: qiskit_aer in /usr/local/lib/python3.11/dist-packages (0.16.0)\n", + "Requirement already satisfied: qiskit>=1.1.0 in /usr/local/lib/python3.11/dist-packages (from qiskit_aer) (1.3.2)\n", + "Requirement already satisfied: numpy>=1.16.3 in /usr/local/lib/python3.11/dist-packages (from qiskit_aer) (1.26.4)\n", + "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.11/dist-packages (from qiskit_aer) (1.13.1)\n", + "Requirement already satisfied: psutil>=5 in /usr/local/lib/python3.11/dist-packages (from qiskit_aer) (5.9.5)\n", + "Requirement already satisfied: rustworkx>=0.15.0 in /usr/local/lib/python3.11/dist-packages (from qiskit>=1.1.0->qiskit_aer) 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(1.17.0)\n", + "Requirement already satisfied: pbr>=2.0.0 in /usr/local/lib/python3.11/dist-packages (from stevedore>=3.0.0->qiskit>=1.1.0->qiskit_aer) (6.1.0)\n", + "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /usr/local/lib/python3.11/dist-packages (from sympy>=1.3->qiskit>=1.1.0->qiskit_aer) (1.3.0)\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "Wb1Bpdad6WBz" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# time_series = pd.read_csv(r\"/content/2025-Moodys/sp500_full.csv\",header=None)\n", + "# time_series=time_series[1][200:400]\n", + "# time_series=np.array(time_series)\n" + ], + "metadata": { + "id": "pNPGu9wm4ttX" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# time_series = pd.read_csv(r\"/content/2025-Moodys/sp500.csv\")\n" + ], + "metadata": { + "id": "W4QlkLCJ5Iew" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "edhTentb5LMm" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit.library import QFT\n", + "from qiskit.circuit.library import UnitaryGate\n", + "import numpy as np\n", + "\n", + "\n", + "def mixed_state_preparation(number_of_target_qubits):\n", + " num_qubits = number_of_target_qubits * 3\n", + " qc = QuantumCircuit(num_qubits, num_qubits, name=\"Custom Circuit\")\n", + "\n", + " # Prepare entangled state between qubits [target_qubits] and [auxiliary_qubits]\n", + " for i in range(number_of_target_qubits, number_of_target_qubits * 2):\n", + " qc.h(i)\n", + "\n", + " output = []\n", + " for i in range(number_of_target_qubits, number_of_target_qubits * 2):\n", + " qc.cx(i, i + number_of_target_qubits) # Ensuring correct pairing\n", + " output.append(i + number_of_target_qubits)\n", + "\n", + " # Measure auxiliary qubits (last set)\n", + " qc.measure(output, output)\n", + "\n", + " return qc\n", + "\n", + "def quantum_phase_estimation(qc, number_of_target_qubits,U):\n", + " # Define U dynamically based on the number of target qubits\n", + " U_gate = UnitaryGate(U, label=\"U\")\n", + "\n", + " # Precision qubits (counting qubits)\n", + " count_bits = list(range(number_of_target_qubits))\n", + "\n", + " # Target qubits (where U applies)\n", + " unary = list(range(number_of_target_qubits, number_of_target_qubits * 2))\n", + "\n", + " # Apply Hadamard gates to precision qubits\n", + " qc.h(count_bits)\n", + "\n", + " # Apply controlled-U^(2^j) operations\n", + " for j in range(number_of_target_qubits - 1, -1, -1):\n", + " power = 2 ** j\n", + " controlled_U = U_gate.power(power).control(1)\n", + "\n", + " qc.append(controlled_U, [count_bits[j]] + unary) # Control qubit j, targets in unary\n", + "\n", + " # Apply inverse Quantum Fourier Transform (QFT†)\n", + " qft_inv = QFT(number_of_target_qubits, do_swaps=False).inverse()\n", + " qc.append(qft_inv, count_bits)\n", + "\n", + " # Measure precision qubits\n", + " qc.measure(count_bits, count_bits)\n", + "\n", + " return qc" + ], + "metadata": { + "id": "IJ3Q2S_0lqaE" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "len(betty_values)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Ohy3F8_f9qVF", + "outputId": "9eb9606c-3b8b-47cd-8ead-b0b5679c9ac4" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "64" + ] + }, + "metadata": {}, + "execution_count": 26 + } + ] + }, + { + "cell_type": "code", + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import gudhi\n", + "from scipy.linalg import expm\n", + "import numpy as np\n", + "\n", + "# Import Qiskit\n", + "from qiskit import QuantumCircuit, transpile\n", + "from qiskit_aer import AerSimulator\n", + "from qiskit.visualization import plot_histogram, plot_state_city\n", + "import qiskit.quantum_info as qi\n", + "time_series = pd.read_csv(r\"/content/2025-Moodys/sp500_full.csv\",header=None)\n", + "time_series=time_series[1]\n", + "time_series = np.log(time_series).to_numpy().squeeze()\n", + "# time_series = np.log(pd.read_csv(r\"/content/2025-Moodys/sp500.csv\", header=None).to_numpy().squeeze())\n", + "\n", + "simulator = AerSimulator()\n", + "\n", + "betty_value_per_epsilon =[]\n", + "for epsilon in np.arange(0.1,0.2,0.1): # Ensure the upper bound is inclusive\n", + " point_cloud = generate_point_cloud(time_series, N=4, d=5, w=5)\n", + " print()\n", + " grouped_simplices_per_filtration = generate_simplex_groups(point_cloud, epsilon)\n", + "\n", + " betty_values= generate_U(grouped_simplices_per_filtration)\n", + " print(betty_values)\n", + " betty_value_per_epsilon.append(betty_values)\n", + "\n", + "\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "-avQfd-ezBgl", + "outputId": "b25ecc08-00ea-4ae7-eecc-5108b49ae19d" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\u001b[1;30;43mStreaming output truncated to the last 5000 lines.\u001b[0m\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1494\n", + "Estimated Betti Number: 1.1953\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0977\n", + "Estimated Betti Number: 0.7812\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1494\n", + "Estimated Betti Number: 1.1953\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1475\n", + "Estimated Betti Number: 1.1797\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1055\n", + "Estimated Betti Number: 0.8438\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1621\n", + "Estimated Betti Number: 1.2969\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1055\n", + "Estimated Betti Number: 0.8438\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0977\n", + "Estimated Betti Number: 0.7812\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1494\n", + "Estimated Betti Number: 1.1953\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1484\n", + "Estimated Betti Number: 1.1875\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1006\n", + "Estimated Betti Number: 0.8047\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1504\n", + "Estimated Betti Number: 1.2031\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1006\n", + "Estimated Betti Number: 0.8047\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1484\n", + "Estimated Betti Number: 1.1875\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1484\n", + "Estimated Betti Number: 1.1875\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1494\n", + "Estimated Betti Number: 1.1953\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0986\n", + "Estimated Betti Number: 0.7891\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0986\n", + "Estimated Betti Number: 0.7891\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0879\n", + "Estimated Betti Number: 0.7031\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1455\n", + "Estimated Betti Number: 1.1641\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1006\n", + "Estimated Betti Number: 0.8047\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1582\n", + "Estimated Betti Number: 1.2656\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1016\n", + "Estimated Betti Number: 0.8125\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1016\n", + "Estimated Betti Number: 0.8125\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1455\n", + "Estimated Betti Number: 1.1641\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1055\n", + "Estimated Betti Number: 0.8438\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1572\n", + "Estimated Betti Number: 1.2578\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1484\n", + "Estimated Betti Number: 1.1875\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1445\n", + "Estimated Betti Number: 1.1562\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1484\n", + "Estimated Betti Number: 1.1875\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0918\n", + "Estimated Betti Number: 0.7344\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1475\n", + "Estimated Betti Number: 1.1797\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0986\n", + "Estimated Betti Number: 0.7891\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", 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8\n", 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8\n", 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1455\n", + "Estimated Betti Number: 1.1641\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1523\n", + "Estimated Betti Number: 1.2188\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1504\n", + "Estimated Betti Number: 1.2031\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1377\n", + "Estimated Betti Number: 1.1016\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0977\n", + "Estimated Betti Number: 0.7812\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.0986\n", + "Estimated Betti Number: 0.7891\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1455\n", + "Estimated Betti Number: 1.1641\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1504\n", + "Estimated Betti Number: 1.2031\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1436\n", + "Estimated Betti Number: 1.1484\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1016\n", + "Estimated Betti Number: 0.8125\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1016\n", + "Estimated Betti Number: 0.8125\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1523\n", + "Estimated Betti Number: 1.2188\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1035\n", + "Estimated Betti Number: 0.8281\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1211\n", + "Estimated Betti Number: 0.9688\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1074\n", + "Estimated Betti Number: 0.8594\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1045\n", + "Estimated Betti Number: 0.8359\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1465\n", + "Estimated Betti Number: 1.1719\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1270\n", + "Estimated Betti Number: 1.0156\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1426\n", + "Estimated Betti Number: 1.1406\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1504\n", + "Estimated Betti Number: 1.2031\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(4, 4)\n", + 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8\n", + "p(0) = 0.2607\n", + "Estimated Betti Number: 2.0859\n", + "(4, 4)\n", + 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8\n", + "p(0) = 0.2539\n", + "Estimated Betti Number: 2.0312\n", + "(4, 4)\n", + 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8\n", + "p(0) = 0.2441\n", + "Estimated Betti Number: 1.9531\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(8, 8)\n", + 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8\n", 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8\n", 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8\n", + "p(0) = 0.0977\n", + "Estimated Betti Number: 0.7812\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1230\n", + "Estimated Betti Number: 0.9844\n", + "(8, 8)\n", + 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8\n", 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8\n", 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(4, 4)\n", + 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8\n", + "p(0) = 0.2412\n", + "Estimated Betti Number: 1.9297\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(8, 8)\n", + 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8\n", 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8\n", 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8\n", 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1523\n", + "Estimated Betti Number: 1.2188\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.0918\n", + "Estimated Betti Number: 0.7344\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1084\n", + "Estimated Betti Number: 0.8672\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1475\n", + "Estimated Betti Number: 1.1797\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1309\n", + "Estimated Betti Number: 1.0469\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1025\n", + "Estimated Betti Number: 0.8203\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1094\n", + "Estimated Betti Number: 0.8750\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1387\n", + "Estimated Betti Number: 1.1094\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1113\n", + "Estimated Betti Number: 0.8906\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1104\n", + "Estimated Betti Number: 0.8828\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1357\n", + "Estimated Betti Number: 1.0859\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1240\n", + "Estimated Betti Number: 0.9922\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1260\n", + "Estimated Betti Number: 1.0078\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1064\n", + "Estimated Betti Number: 0.8516\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1172\n", + "Estimated Betti Number: 0.9375\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1416\n", + "Estimated Betti Number: 1.1328\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1318\n", + "Estimated Betti Number: 1.0547\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1221\n", + "Estimated Betti Number: 0.9766\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1348\n", + "Estimated Betti Number: 1.0781\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1162\n", + "Estimated Betti Number: 0.9297\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1289\n", + "Estimated Betti Number: 1.0312\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1406\n", + "Estimated Betti Number: 1.1250\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1201\n", + "Estimated Betti Number: 0.9609\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1299\n", + "Estimated Betti Number: 1.0391\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1191\n", + "Estimated Betti Number: 0.9531\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1123\n", + "Estimated Betti Number: 0.8984\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(8, 8)\n", + 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8\n", + "p(0) = 0.1367\n", + "Estimated Betti Number: 1.0938\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1250\n", + "Estimated Betti Number: 1.0000\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1152\n", + "Estimated Betti Number: 0.9219\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1338\n", + "Estimated Betti Number: 1.0703\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1182\n", + "Estimated Betti Number: 0.9453\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1279\n", + "Estimated Betti Number: 1.0234\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1143\n", + "Estimated Betti Number: 0.9141\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1396\n", + "Estimated Betti Number: 1.1172\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1328\n", + "Estimated Betti Number: 1.0625\n", + "(16, 16)\n", + 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8\n", + "p(0) = 0.1133\n", + "Estimated Betti Number: 0.9062\n", + "(16, 16)\n", + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888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8\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "U_range = list(map(list, zip(*betty_value_per_epsilon)))\n", + "print(len(U_range),len(U_range[0]))\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "KEea_z3oxdPA", + "outputId": "7231dca8-6505-490d-ec86-ac7f09b92e66" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "64 9\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "components = U_range\n", + "# Calculate distances between components\n", + "components = np.array(components)\n", + "components = np.rint(components).astype(int)\n", + "\n", + "distances = [np.linalg.norm(components[i] - components[i + 1]) for i in range(len(components) - 1)]\n", + "\n", + "# Print distances\n", + "len(distances)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "L9h-pxdpzdIN", + "outputId": "bf07c7be-7c50-4a75-fbb1-f577b3abcb85" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "63" + ] + }, + "metadata": {}, + "execution_count": 16 + } + ] + }, + { + "cell_type": "code", + "source": [ + "components" + ], + "metadata": { + "id": "5bcsUNV72sNr" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Example data: Replace with your actual list of 32 elements\n", + "data=distances\n", + "# Plot the line chart\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot(range(1, 64), data, marker='o', linestyle='-', color='b', label='Data Trend')\n", + "\n", + "# Labels and Title\n", + "plt.xlabel(\"Index\")\n", + "plt.ylabel(\"Value\")\n", + "plt.title(\"Line Chart for 32 Elements\")\n", + "plt.grid(True)\n", + "plt.legend()\n", + "\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 403 + }, + "id": "cK1EcxE50ekW", + "outputId": "981e44ac-5e8f-40a6-b561-840aa449db1d" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "2Tr_ylf6mAgG" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/Program_Quantum_Load.ipynb b/Program_Quantum_Load.ipynb new file mode 100644 index 0000000..9f54a9e --- /dev/null +++ b/Program_Quantum_Load.ipynb @@ -0,0 +1,1003 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "cFAMXPSwxjvI", + "outputId": "9a319193-c55d-4849-9bca-cc25c3389ddd" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fatal: destination path '2025-Moodys' already exists and is not an empty directory.\n", + "Requirement already satisfied: giotto-tda in /opt/conda/lib/python3.11/site-packages (0.6.2)\n", + "Requirement already satisfied: numpy>=1.19.1 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (1.26.4)\n", + "Requirement already satisfied: scipy>=1.5.0 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (1.15.1)\n", + "Requirement already satisfied: joblib>=0.16.0 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (1.4.2)\n", + "Requirement already satisfied: scikit-learn==1.3.2 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (1.3.2)\n", + "Requirement already satisfied: giotto-ph>=0.2.1 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (0.2.4)\n", + "Requirement already satisfied: pyflagser>=0.4.3 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (0.4.7)\n", + "Requirement already satisfied: igraph>=0.9.8 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (0.11.8)\n", + "Requirement already satisfied: plotly>=4.8.2 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (6.0.0)\n", + "Requirement already satisfied: ipywidgets>=7.5.1 in /opt/conda/lib/python3.11/site-packages (from giotto-tda) (8.1.5)\n", + "Requirement 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}, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "ugOpPkrRlorV" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "bsvOLdZ1x1m8" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(150,)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "\n", + "time_series = pd.read_csv(r\"sp500_full.csv\", header=None)\n", + "time_series = np.log(time_series[1][150:300]).to_numpy().squeeze()\n", + "time_series.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "gbPIe2CYx3O2" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "def takens_embedding(time_series, N, d):\n", + "\n", + " L = len(time_series)\n", + " Z = []\n", + "\n", + " for t in range(L - (N - 1) * d):\n", + " z_t = [time_series[t + i * d] for i in range(N)]\n", + " Z.append(z_t)\n", + "\n", + " return np.array(Z)\n", + "\n", + "def sliding_window(point_cloud, w):\n", + "\n", + " K = len(point_cloud) - w + 1\n", + " windows = []\n", + "\n", + " for t in range(K):\n", + " Z_t = point_cloud[t:t + w]\n", + " windows.append(Z_t)\n", + "\n", + " return windows\n", + "\n", + "\n", + "\n", + "\n", + "def generate_boundary_operator(simplex_tree, k):\n", + " \"\"\"\n", + " Generates the boundary operator matrix ∂_k for a simplicial complex represented by a simplex tree.\n", + "\n", + " Args:\n", + " simplex_tree: A simplex tree data structure containing ordered simplices.\n", + " k (int): The dimension of the simplices for which to compute the boundary operator.\n", + "\n", + " Returns:\n", + " np.ndarray: A sparse matrix where entry [i][j] is the coefficient of the (k-1)-simplex i\n", + " in the boundary of the k-simplex j.\n", + " \"\"\"\n", + " # Edge case: boundary of 0-simplices is trivial\n", + " if k == 0:\n", + " return np.zeros((0, len(simplex_tree[k]))) # Empty matrix\n", + "\n", + " # Extract ordered lists of k-simplices and (k-1)-simplices\n", + " k_simplices = simplex_tree[k] # Columns of the matrix\n", + " km1_simplices = simplex_tree[k-1] # Rows of the matrix\n", + "\n", + " # Create a dictionary to map (k-1)-simplices to their row indices\n", + " km1_simplex_to_index = {tuple(s): idx for idx, s in enumerate(km1_simplices)}\n", + "\n", + " # Initialize the boundary matrix with zeros\n", + " boundary_matrix = np.zeros((len(km1_simplices), len(k_simplices)), dtype=int)\n", + "\n", + " # Iterate over each k-simplex (column j)\n", + " for j, s_k in enumerate(k_simplices):\n", + " # Remove each vertex at position t and compute the boundary\n", + " for t in range(len(s_k)):\n", + " # Generate the (k-1)-simplex by removing vertex t\n", + " s_km1 = tuple(s_k[:t] + s_k[t+1:])\n", + "\n", + " # Get the row index for this (k-1)-simplex\n", + " if s_km1 in km1_simplex_to_index:\n", + " i = km1_simplex_to_index[s_km1]\n", + " # Assign coefficient (-1)^t to matrix entry [i][j]\n", + " boundary_matrix[i][j] = (-1) ** t\n", + "\n", + " return boundary_matrix\n", + "\n", + "def generate_k_laplasian_matrix(grouped_simplices_per_filtration,k,i_simplice):\n", + " simplextree_zero = grouped_simplices_per_filtration[i_simplice]\n", + " boundary_1=generate_boundary_operator(simplextree_zero, k)\n", + " partial_1=np.dot(boundary_1.T,boundary_1)\n", + " if len(simplextree_zero)==2:\n", + " return partial_1\n", + " boundary_2=generate_boundary_operator(simplextree_zero, k+1)\n", + " partial_2=np.dot(boundary_2,boundary_2.T)\n", + " delta1=partial_1+partial_2\n", + " return delta1\n", + "\n", + "def is_power_of_two(n):\n", + " \"\"\"Check if n is a power of two.\"\"\"\n", + " return n != 0 and (n & (n - 1)) == 0\n", + "\n", + "def next_power_of_two(n):\n", + " \"\"\"Find the smallest power of two greater than or equal to n.\"\"\"\n", + " if n == 0:\n", + " return 1\n", + " return 1 << (n - 1).bit_length()\n", + "\n", + "def pad_matrix_to_power_of_two(matrix):\n", + "\n", + " n = len(matrix)\n", + " # Validate the matrix is square\n", + " for row in matrix:\n", + " if len(row) != n:\n", + " raise ValueError(\"Matrix must be square.\")\n", + "\n", + " # Calculate the next power of two and its exponent k\n", + " m = next_power_of_two(n)\n", + " k = m.bit_length() - 1 # Since m is 2^k\n", + "\n", + " # Create a new matrix filled with zeros\n", + " padded_matrix = [[0] * m for _ in range(m)]\n", + "\n", + " # Copy the original matrix into the top-left corner\n", + " for i in range(n):\n", + " for j in range(n):\n", + " padded_matrix[i][j] = matrix[i][j]\n", + "\n", + " # Fill the new diagonal elements with k\n", + " for i in range(n, m):\n", + " padded_matrix[i][i] = k\n", + "\n", + " return padded_matrix\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "RD-tUN694qLu" + }, + "outputs": [], + "source": [ + "#step 1\n", + "def generate_point_cloud(time_series, N, d, w):\n", + "\n", + " Z = takens_embedding(time_series, N, d)\n", + " point_cloud = sliding_window(Z, w)\n", + "\n", + " return point_cloud\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "WiLZyy7-3lom" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: qiskit in /opt/conda/lib/python3.11/site-packages (1.3.2)\n", + "Requirement already satisfied: qiskit-ionq in /opt/conda/lib/python3.11/site-packages (0.5.12)\n", + "Requirement already satisfied: rustworkx>=0.15.0 in /opt/conda/lib/python3.11/site-packages (from qiskit) (0.16.0)\n", + "Requirement already satisfied: numpy<3,>=1.17 in /opt/conda/lib/python3.11/site-packages (from qiskit) (1.26.4)\n", + "Requirement already satisfied: scipy>=1.5 in /opt/conda/lib/python3.11/site-packages (from qiskit) (1.15.1)\n", + "Requirement already satisfied: sympy>=1.3 in 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/opt/conda/lib/python3.11/site-packages (from qiskit-ionq) (7.1.0)\n", + "Requirement already satisfied: python-dotenv>=1.0.1 in /opt/conda/lib/python3.11/site-packages (from qiskit-ionq) (1.0.1)\n", + "Requirement already satisfied: zipp>=0.5 in /opt/conda/lib/python3.11/site-packages (from importlib-metadata>=4.11.4->qiskit-ionq) (3.17.0)\n", + "Requirement already satisfied: six>=1.5 in /opt/conda/lib/python3.11/site-packages (from python-dateutil>=2.8.0->qiskit) (1.16.0)\n", + "Requirement already satisfied: charset-normalizer<4,>=2 in /opt/conda/lib/python3.11/site-packages (from requests>=2.24.0->qiskit-ionq) (3.3.2)\n", + "Requirement already satisfied: idna<4,>=2.5 in /opt/conda/lib/python3.11/site-packages (from requests>=2.24.0->qiskit-ionq) (3.7)\n", + "Requirement already satisfied: urllib3<3,>=1.21.1 in /opt/conda/lib/python3.11/site-packages (from requests>=2.24.0->qiskit-ionq) (2.2.1)\n", + "Requirement already satisfied: certifi>=2017.4.17 in /opt/conda/lib/python3.11/site-packages (from requests>=2.24.0->qiskit-ionq) (2024.2.2)\n", + "Requirement already satisfied: pbr>=2.0.0 in /opt/conda/lib/python3.11/site-packages (from stevedore>=3.0.0->qiskit) (6.1.0)\n", + "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /opt/conda/lib/python3.11/site-packages (from sympy>=1.3->qiskit) (1.3.0)\n", + "[, , ]\n" + ] + }, + { + "data": { + "text/plain": [ + "{'device_id': 'ibm_kyiv',\n", + " 'simulator': False,\n", + " 'num_qubits': 127,\n", + " 'provider_name': 'IBM',\n", + " 'basis_gates': None,\n", + " 'local': False,\n", + " 'instance': 'ibm-q/open/main',\n", + " 'max_shots': 100000,\n", + " 'queue_depth': 2,\n", + " 'status': 'ONLINE',\n", + " 'paradigm': None,\n", + " 'runtime_config': {'target_ir': 'qiskit',\n", + " 'conversion_scheme': {'conversion_graph': None,\n", + " 'max_path_attempts': 3,\n", + " 'max_path_depth': None},\n", + " 'options': {'transpile': True,\n", + " 'transform': True,\n", + " 'validate': 2,\n", + " 'prepare': True,\n", + " 'pass_manager': None}}}" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "!pip install qiskit qiskit-ionq\n", + "from qbraid.runtime import QiskitRuntimeProvider\n", + "from qiskit import transpile\n", + "from qiskit_ibm_runtime import Sampler\n", + "\n", + "provider = QiskitRuntimeProvider(\"c7aa35798b4a69664d1529bc5e8ace456e2287509a9ce9631089c37672c4297570128da37f222d875c3dc12b9de9cc48ac9728785ed9fa5dd636839851c671df\")\n", + "\n", + "print(provider.get_devices())\n", + "\n", + "device = provider.get_device('ibm_kyiv')\n", + "\n", + "type(device)\n", + "# qbraid.runtime.ibm.device.QiskitBackend\n", + "\n", + "device.metadata()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "sCsEt3t_4un1" + }, + "outputs": [], + "source": [ + " #step 2\n", + "def bitstring_to_phase(bitstring):\n", + " return int(bitstring, 2) / (2 ** len(bitstring))\n", + "def generate_simplex_groups(point_cloud,epsilon):\n", + " grouped_simplices_per_filtration = []\n", + "\n", + " for cloud in point_cloud:\n", + " rips_complex = gudhi.RipsComplex(points=cloud, max_edge_length=epsilon)\n", + " simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)\n", + "\n", + " filtration = simplex_tree.get_filtration()\n", + " grouped_simplices = {}\n", + "\n", + " for simplex, _ in filtration:\n", + " dim = len(simplex) - 1 # Dimension of the simplex\n", + " if dim not in grouped_simplices:\n", + " grouped_simplices[dim] = []\n", + " grouped_simplices[dim].append(simplex)\n", + "\n", + " # Convert dictionary to sorted list of lists (by dimension)\n", + " grouped_simplices_per_filtration.append([grouped_simplices[dim] for dim in sorted(grouped_simplices.keys())])\n", + "\n", + " # Output the list of lists for each filtration\n", + " # for idx, filtration in enumerate(grouped_simplices_per_filtration):\n", + " # print(f\"Filtration {idx}: {filtration}\")\n", + " return grouped_simplices_per_filtration\n", + "import math\n", + "def generate_U(grouped_simplices_per_filtration):\n", + " betty_value_per_cloud=[]\n", + " for i in range(len(grouped_simplices_per_filtration)):\n", + " delta=generate_k_laplasian_matrix(grouped_simplices_per_filtration,1,i)\n", + " H=np.array(pad_matrix_to_power_of_two(delta))\n", + " iH = 1j * H\n", + " U = expm(iH)\n", + " number_of_target_qubits = int(math.log2(U.shape[0]))\n", + " print(U.shape)\n", + " mixed_state_circuit = mixed_state_preparation(number_of_target_qubits)\n", + " qpe_circuit = quantum_phase_estimation(mixed_state_circuit, number_of_target_qubits,U)\n", + " job = device.run(qpe_circuit, shots=1024)\n", + "\n", + " result = job.result()\n", + " counts = result.data.get_counts()\n", + " print(\"Measurement counts:\", counts)\n", + "\n", + "\n", + " # Convert the bitstrings from the result\n", + " phase_estimates = [bitstring_to_phase(bitstring) for bitstring in result.get_counts().keys()]\n", + " alpha = sum(counts.values())\n", + "\n", + " # Count occurrences of '000' in the first three qubits\n", + " zero_state_count = sum(v for k, v in counts.items() if k[:3] == '000')\n", + "\n", + " # Compute probability p(0)\n", + " p_0 = zero_state_count / alpha\n", + " print(f\"p(0) = {p_0:.4f}\")\n", + "\n", + "\n", + " q = 3 # Number of qubits for phase estimation\n", + " beta_k_tilde = (2**q) * p_0\n", + " print(f\"Estimated Betti Number: {beta_k_tilde:.4f}\")\n", + " betty_value_per_cloud.append(beta_k_tilde)\n", + "\n", + " return betty_value_per_cloud" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "id": "70bOxzI7ogRY" + }, + "outputs": [], + "source": [ + "def generate_betti_numbers(grouped_simplices_per_filtration, q=5): # Adjust q as needed\n", + " betti_numbers = []\n", + " for i in range(len(grouped_simplices_per_filtration)):\n", + " # Generate Laplacian for k=1 at filtration step i\n", + " laplacian = generate_k_laplasian_matrix(grouped_simplices_per_filtration, k=1, i_simplice=i)\n", + "\n", + " # Pad to power-of-two and normalize eigenvalues\n", + " padded_laplacian = pad_matrix_to_power_of_two(laplacian)\n", + " max_eigenvalue = np.linalg.norm(padded_laplacian, 2) # Spectral norm\n", + " H = padded_laplacian / max_eigenvalue * 2 * np.pi # Scale eigenvalues to [0, 2π)\n", + "\n", + " # Construct unitary U = e^(iH)\n", + " U = expm(1j * H)\n", + "\n", + " # Determine target qubits\n", + " num_target_qubits = int(np.log2(U.shape[0]))\n", + "\n", + " # Prepare uniform superposition state (not mixed)\n", + " state_prep_circuit = mixed_state_preparation(num_target_qubits)\n", + "\n", + " # Quantum Phase Estimation\n", + " qpe_circuit = quantum_phase_estimation(state_prep_circuit, num_target_qubits, U)\n", + " job = device.run(qpe_circuit, shots=1024)\n", + "\n", + " result = job.result()\n", + " counts = result.data.get_counts()\n", + " print(\"Measurement counts:\", counts)\n", + "\n", + " # Estimate Betti number: count zero phases and scale\n", + " zero_phase_counts = sum(v for k, v in counts.items() if k.startswith('0'*q))\n", + " p_0 = zero_phase_counts / sum(counts.values())\n", + " betti = p_0 * (2 ** num_target_qubits)\n", + " print(f\"Estimated Betti Number: {betti:.4f}\")\n", + " betti_numbers.append(betti)\n", + "\n", + " return betti_numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "MIBCNZzunJO4" + }, + "outputs": [], + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit.library import QFT\n", + "from qiskit.circuit.library import UnitaryGate\n", + "import numpy as np\n", + "\n", + "\n", + "def mixed_state_preparation(number_of_target_qubits):\n", + " num_qubits = number_of_target_qubits*3\n", + " qc = QuantumCircuit(num_qubits, num_qubits, name=\"Custom Circuit\")\n", + "\n", + " # Prepare entangled state between qubits 3-5 and 6-8\n", + " for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + " qc.h(i)\n", + "\n", + " output = []\n", + " for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + " qc.cx(i, i+3)\n", + " output.append(i+number_of_target_qubits)\n", + "\n", + " # Measure auxiliary qubits (3-5)\n", + " print(output)\n", + " qc.measure(output, output)\n", + "\n", + " return qc\n", + "\n", + "# def quantum_phase_estimation(qc, U_i ,number_of_target_qubits):\n", + "# U_gate = UnitaryGate(U_i, label=\"U\")\n", + "\n", + "# # Apply Hadamard to precision qubits (0-2)\n", + "# for i in range(number_of_target_qubits):\n", + "# qc.h(i)\n", + "\n", + "# count_bits = []\n", + "# unary = []\n", + "\n", + "# for i in range(number_of_target_qubits, number_of_target_qubits*2):\n", + "# unary.append(i)\n", + "\n", + "# # Apply controlled-U^(2^j) operations\n", + "# for j in range(number_of_target_qubits-1,-1,-1):\n", + "# print(j)\n", + "# power = 2 ** j\n", + "# count_bits.append(j)\n", + "# controlled_U = U_gate.power(power).control(1)\n", + "\n", + "# qc.append(controlled_U, [number_of_target_qubits-j-1]+unary) # Control qubit j, targets 6-8\n", + "\n", + "# # Apply inverse QFT on precision qubits\n", + "# qft_inv = QFT(number_of_target_qubits, do_swaps=False).inverse()\n", + "# qc.append(qft_inv, count_bits)\n", + "\n", + "# # Measure precision qubits\n", + "# qc.measure(count_bits, count_bits)\n", + "\n", + "# return qc\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "WLtZmeRxp81B", + "outputId": "56fee359-88f0-4ec7-c0a8-eaf9883c88b0" + }, + "outputs": [], + "source": [ + "# !pip install qiskit_aer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "Wb1Bpdad6WBz" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "id": "pNPGu9wm4ttX" + }, + "outputs": [], + "source": [ + "# time_series = pd.read_csv(r\"/content/2025-Moodys/sp500_full.csv\",header=None)\n", + "# time_series=time_series[1][200:400]\n", + "# time_series=np.array(time_series)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "id": "W4QlkLCJ5Iew" + }, + "outputs": [], + "source": [ + "# time_series = pd.read_csv(r\"/content/2025-Moodys/sp500.csv\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "edhTentb5LMm" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "id": "IJ3Q2S_0lqaE" + }, + "outputs": [], + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit.library import QFT\n", + "from qiskit.circuit.library import UnitaryGate\n", + "import numpy as np\n", + "\n", + "\n", + "def mixed_state_preparation(number_of_target_qubits):\n", + " num_qubits = number_of_target_qubits * 3\n", + " qc = QuantumCircuit(num_qubits, num_qubits, name=\"Custom Circuit\")\n", + "\n", + " # Prepare entangled state between qubits [target_qubits] and [auxiliary_qubits]\n", + " for i in range(number_of_target_qubits, number_of_target_qubits * 2):\n", + " qc.h(i)\n", + "\n", + " output = []\n", + " for i in range(number_of_target_qubits, number_of_target_qubits * 2):\n", + " qc.cx(i, i + number_of_target_qubits) # Ensuring correct pairing\n", + " output.append(i + number_of_target_qubits)\n", + "\n", + " # Measure auxiliary qubits (last set)\n", + " qc.measure(output, output)\n", + "\n", + " return qc\n", + "\n", + "def quantum_phase_estimation(qc, number_of_target_qubits,U):\n", + " # Define U dynamically based on the number of target qubits\n", + " U_gate = UnitaryGate(U, label=\"U\")\n", + "\n", + " # Precision qubits (counting qubits)\n", + " count_bits = list(range(number_of_target_qubits))\n", + "\n", + " # Target qubits (where U applies)\n", + " unary = list(range(number_of_target_qubits, number_of_target_qubits * 2))\n", + "\n", + " # Apply Hadamard gates to precision qubits\n", + " qc.h(count_bits)\n", + "\n", + " # Apply controlled-U^(2^j) operations\n", + " for j in range(number_of_target_qubits - 1, -1, -1):\n", + " power = 2 ** j\n", + " controlled_U = U_gate.power(power).control(1)\n", + "\n", + " qc.append(controlled_U, [count_bits[j]] + unary) # Control qubit j, targets in unary\n", + "\n", + " # Apply inverse Quantum Fourier Transform (QFT†)\n", + " qft_inv = QFT(number_of_target_qubits, do_swaps=False).inverse()\n", + " qc.append(qft_inv, count_bits)\n", + "\n", + " # Measure precision qubits\n", + " qc.measure(count_bits, count_bits)\n", + "\n", + " return qc" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "-avQfd-ezBgl", + "outputId": "e4623299-f547-460f-f046-589857b0f193" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Measurement counts: {'000000000000001101011': 1, '000000100000000001001': 1, '000000100000000011100': 1, '000000100000000100111': 1, '000000100000000101000': 1, '000000100000000101011': 1, '000000100000000101100': 2, '000000100000000110110': 1, '000000100000000111010': 1, '000000100000000111100': 1, '000000100000001000100': 1, '000000100000001000111': 1, '000000100000001010100': 1, '000000100000001011001': 2, '000000100000001011010': 1, '000000100000001100000': 2, '000000100000001100010': 1, '000000100000001100100': 1, '000000100000001100101': 1, '000000100000001101010': 1, '000000100000001110001': 1, '000000100000001110010': 1, '000000100000001110011': 2, '000000100000001110101': 1, '000000100000001110110': 1, '000000100000001111000': 1, '000000100000001111101': 1, '000001000000001000111': 1, '000001100000000000001': 1, '000001100000000001010': 1, '000001100000000001111': 1, '000001100000000010011': 2, '000001100000000010110': 1, '000001100000000011010': 1, '000001100000000011111': 1, '000001100000000101001': 1, '000001100000001000110': 2, '000001100000001001000': 1, '000001100000001001011': 1, '000001100000001001111': 1, '000001100000001010011': 1, '000001100000001010100': 1, '000001100000001011000': 1, '000001100000001011010': 1, '000001100000001100000': 1, '000001100000001100011': 1, '000001100000001101010': 1, '000001100000001101101': 2, '000001100000001101110': 1, '000001100000001110110': 1, '000001100000001111100': 3, '000001100000001111101': 3, '000001100000001111110': 1, '000010000000000101001': 1, '000010000000001100001': 1, '000010000000001111100': 1, '000010100000000010001': 1, '000010100000000010101': 1, '000010100000000011001': 1, '000010100000000011110': 1, '000010100000000101101': 1, '000010100000000101111': 1, '000010100000000111000': 2, '000010100000000111010': 1, '000010100000000111100': 1, '000010100000000111111': 2, '000010100000001001000': 1, '000010100000001001001': 1, '000010100000001001100': 2, '000010100000001010000': 1, '000010100000001010100': 1, '000010100000001010101': 1, '000010100000001011001': 1, '000010100000001011101': 1, '000010100000001100110': 1, '000010100000001101000': 1, '000010100000001101011': 1, '000010100000001101110': 1, '000010100000001110100': 2, '000010100000001110110': 1, '000010100000001111010': 1, '000011000000001011101': 1, '000011100000000000000': 1, '000011100000000001011': 2, '000011100000000001100': 1, '000011100000000011111': 1, '000011100000000100000': 1, '000011100000000100001': 1, '000011100000000100111': 2, '000011100000000110100': 1, '000011100000000111000': 1, '000011100000000111011': 1, '000011100000000111111': 1, '000011100000001000110': 1, '000011100000001001000': 1, '000011100000001001001': 1, '000011100000001001010': 1, '000011100000001001011': 1, '000011100000001001101': 1, '000011100000001001110': 1, '000011100000001001111': 1, '000011100000001010001': 1, '000011100000001010100': 1, '000011100000001010111': 1, '000011100000001011010': 1, '000011100000001011111': 1, '000011100000001100001': 1, '000011100000001100010': 1, '000011100000001100101': 1, '000011100000001101001': 2, '000011100000001101011': 2, '000011100000001101100': 1, '000011100000001101111': 1, '000011100000001110000': 1, '000011100000001110010': 1, '000011100000001110100': 1, '000011100000001110111': 1, '000011100000001111100': 2, '000011100000001111101': 1, '000100000000000101101': 1, '000100000000001001101': 1, '000100100000000000100': 1, '000100100000000010100': 1, '000100100000000100001': 1, '000100100000000100101': 1, '000100100000000100111': 1, '000100100000000101101': 1, '000100100000001000000': 1, '000100100000001000001': 2, '000100100000001000011': 1, '000100100000001000110': 1, '000100100000001001111': 1, '000100100000001010010': 1, '000100100000001010011': 1, '000100100000001011010': 1, '000100100000001011110': 1, '000100100000001100101': 1, '000100100000001100110': 1, '000100100000001101001': 1, '000100100000001101010': 1, '000100100000001110001': 1, '000100100000001110010': 1, '000100100000001110110': 2, '000100100000001111000': 3, '000100100000001111001': 1, '000100100000001111101': 1, '000100100000001111111': 1, '000101100000000000010': 2, '000101100000000001101': 1, '000101100000000010001': 1, '000101100000000011101': 1, '000101100000000100011': 1, '000101100000000100100': 1, '000101100000000101101': 1, '000101100000000110101': 1, '000101100000000110111': 1, '000101100000000111000': 1, '000101100000000111101': 1, '000101100000000111110': 1, '000101100000001000111': 1, '000101100000001001000': 1, '000101100000001001010': 2, '000101100000001001011': 1, '000101100000001001111': 1, '000101100000001010010': 1, '000101100000001011110': 1, '000101100000001100010': 1, '000101100000001100100': 1, '000101100000001100101': 1, '000101100000001100111': 1, '000101100000001101001': 1, '000101100000001101111': 1, '000101100000001110001': 1, '000101100000001110010': 1, '000101100000001111001': 1, 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'110101100000001100110': 2, '110101100000001100111': 1, '110101100000001101010': 1, '110101100000001101011': 1, '110101100000001101100': 1, '110101100000001101101': 1, '110101100000001101111': 1, '110101100000001110000': 1, '110101100000001110001': 1, '110101100000001110010': 1, '110101100000001110110': 1, '110101100000001111101': 2, '110110000000000101100': 1, '110110100000000000100': 1, '110110100000000001011': 1, '110110100000000001110': 1, '110110100000000010101': 1, '110110100000000010110': 1, '110110100000000011101': 1, '110110100000000101110': 1, '110110100000000110100': 2, '110110100000000110110': 1, '110110100000000111001': 1, '110110100000000111010': 1, '110110100000000111111': 1, '110110100000001001100': 1, '110110100000001001111': 1, '110110100000001010100': 1, '110110100000001011100': 1, '110110100000001100011': 1, '110110100000001110000': 1, '110110100000001111010': 1, '110110100000001111100': 1, '110111000000001110001': 1, '110111100000000001000': 1, '110111100000000010010': 1, '110111100000000100101': 1, '110111100000000101011': 1, '110111100000000111101': 1, '110111100000000111111': 1, '110111100000001000101': 1, '110111100000001000110': 1, '110111100000001001010': 1, '110111100000001001011': 1, '110111100000001001100': 1, '110111100000001010001': 1, '110111100000001010111': 1, '110111100000001011001': 1, '110111100000001011100': 1, '110111100000001011101': 1, '110111100000001100010': 1, '110111100000001100111': 1, '110111100000001101000': 1, '110111100000001101110': 2, '110111100000001110101': 1, '110111100000001110110': 1, '110111100000001110111': 1, '110111100000001111101': 1, '111000100000000111000': 1}\n", + "Estimated Betti Number: 8.0000\n", + "Measurement counts: {'000000100000000000010': 1, '000000100000000001010': 1, '000000100000000001101': 1, '000000100000000010101': 1, '000000100000000011011': 1, '000000100000000011110': 1, '000000100000000100001': 2, '000000100000000100100': 1, '000000100000000100110': 1, 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'111100100000000001000': 1, '111100100000000010010': 1, '111100100000000101000': 1, '111100100000000101100': 1, '111100100000000110100': 1, '111100100000000111111': 1, '111100100000001000110': 1, '111100100000001011001': 1, '111101100000000001101': 1, '111101100000001000010': 1, '111101100000001010001': 1, '111101100000001011001': 1, '111110100000000000100': 1, '111110100000000000111': 1, '111110100000000001011': 1, '111110100000000010010': 1, '111110100000000011101': 1, '111110100000000110000': 1, '111110100000000111001': 1, '111110100000001000000': 1, '111110100000001010101': 1, '111110100000001011100': 1, '111110100000001100101': 1, '111110100000001101100': 2, '111111100000000001011': 1, '111111100000000010000': 1, '111111100000000010100': 1, '111111100000001000000': 1, '111111100000001101001': 1, '111111100000001101111': 1, '111111100000001110101': 1, '111111100000001111110': 1}\n", + "Estimated Betti Number: 6.7500\n", + "Measurement counts: {'000000000000000001000': 1, 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'111101000000000100011': 1, '111101000000000111111': 1, '111101000000001000001': 1, '111101000000001001101': 1, '111101000000001010001': 1, '111101000000001010101': 1, '111101000000001100100': 1, '111101000000001111000': 1, '111101100000000000011': 1, '111101100000000000100': 1, '111101100000000001011': 1, '111101100000000011011': 1, '111101100000000011111': 1, '111101100000001000101': 1, '111101100000001001001': 1, '111101100000001101010': 1, '111101100000001101011': 1, '111110000000000010010': 1, '111110000000000011011': 1, '111110000000000100110': 1, '111110000000000110000': 1, '111110000000001000110': 1, '111110000000001001100': 1, '111110000000001001110': 1, '111110000000001011110': 1, '111110000000001100011': 1, '111110100000000000011': 1, '111110100000000000110': 1, '111110100000000100011': 1, '111110100000000110000': 1, '111110100000000110100': 1, '111110100000000111001': 1, '111110100000001001001': 1, '111110100000001011010': 1, '111110100000001011110': 1, '111110100000001110000': 1, '111110100000001111101': 1, '111111000000000011111': 1, '111111000000000100110': 1, '111111000000000110000': 1, '111111000000001001011': 1, '111111000000001100110': 1, '111111000000001101111': 1, '111111100000000110001': 1, '111111100000000111010': 1, '111111100000001010001': 1, '111111100000001100111': 1}\n", + "Estimated Betti Number: 4.5000\n", + "Measurement counts: {'000000000000000101100': 1, '000000000000001000101': 1, '000000000000001010001': 1, '000000000000001101010': 1, '000000100000000010010': 1, '000000100000000100000': 1, '000000100000000100010': 1, '000000100000000110011': 1, '000000100000001011000': 1, '000000100000001011011': 1, '000000100000001110000': 1, '000001000000000001011': 1, '000001000000000001111': 1, '000001000000000010001': 1, '000001000000000100111': 1, '000001000000001010000': 1, '000001000000001101101': 1, '000001000000001110000': 1, '000001100000000000101': 1, '000001100000000010001': 1, '000001100000001010100': 1, 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'111010100000001000110': 1, '111010100000001001000': 1, '111010100000001001011': 1, '111010100000001010000': 1, '111010100000001010101': 1, '111010100000001010110': 1, '111010100000001010111': 1, '111010100000001011100': 1, '111010100000001100000': 1, '111010100000001101001': 1, '111010100000001110101': 1, '111010100000001111001': 1, '111010100000001111100': 1, '111011000000000000000': 1, '111011000000000000111': 1, '111011000000000001011': 1, '111011000000000001111': 1, '111011000000000011000': 1, '111011000000000011111': 1, '111011000000000100001': 1, '111011000000000101010': 1, '111011000000000101100': 1, '111011000000000101110': 2, '111011000000000111101': 1, '111011000000000111111': 1, '111011000000001000010': 1, '111011000000001001000': 1, '111011000000001001001': 1, '111011000000001001011': 1, '111011000000001001101': 1, '111011000000001010000': 1, '111011000000001011111': 1, '111011000000001100001': 1, '111011000000001101000': 1, '111011000000001101001': 2, '111011000000001101011': 1, '111011000000001101100': 1, '111011000000001110101': 1, '111011100000000000000': 1, '111011100000000000010': 1, '111011100000000000011': 1, '111011100000000000111': 1, '111011100000000001010': 1, '111011100000000001011': 1, '111011100000000010001': 1, '111011100000000010110': 1, '111011100000000011100': 2, '111011100000000100001': 1, '111011100000000110010': 1, '111011100000000110011': 1, '111011100000000111010': 1, '111011100000000111110': 1, '111011100000001000110': 1, '111011100000001001010': 1, '111011100000001001011': 1, '111011100000001010011': 1, '111011100000001011011': 1, '111011100000001100101': 1, '111011100000001101001': 1, '111011100000001101110': 1, '111011100000001110000': 1, '111011100000001111000': 1, '111011100000001111111': 1, '111101000000001000010': 1}\n", + "Estimated Betti Number: 2.8750\n", + "Measurement counts: {'000000000000000000001': 1, '000000000000000111011': 1, '000001000000000000010': 1, '000001000000000000110': 1, 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'011001000000001110011': 1, '011001000000001110100': 1, '011001000000001110110': 1, '011001000000001110111': 2, '011001000000001111000': 1, '011001000000001111001': 2, '011001000000001111011': 1, '011001000000001111100': 1, '011001000000001111111': 1, '011011000000000000001': 1, '011011000000000000011': 1, '011011000000000001001': 1, '011011000000000001010': 1, '011011000000000001011': 2, '011011000000000001101': 3, '011011000000000001110': 1, '011011000000000001111': 1, '011011000000000010001': 1, '011011000000000010101': 1, '011011000000000011010': 1, '011011000000000011100': 1, '011011000000000011101': 2, '011011000000000011110': 1, '011011000000000011111': 2, '011011000000000100001': 2, '011011000000000100011': 1, '011011000000000100100': 1, '011011000000000100110': 1, '011011000000000101001': 1, '011011000000000101010': 1, '011011000000000101100': 2, '011011000000000101101': 1, '011011000000000101111': 2, '011011000000000110001': 1, '011011000000000110100': 1, '011011000000000111000': 1, '011011000000000111011': 4, '011011000000000111100': 3, '011011000000000111101': 1, '011011000000001000001': 1, '011011000000001000011': 1, '011011000000001001001': 1, '011011000000001001101': 2, '011011000000001010000': 1, '011011000000001010001': 1, '011011000000001010010': 1, '011011000000001010100': 1, '011011000000001010101': 1, '011011000000001011100': 1, '011011000000001011101': 1, '011011000000001011111': 2, '011011000000001100100': 1, '011011000000001101000': 1, '011011000000001101100': 1, '011011000000001101101': 1, '011011000000001101110': 1, '011011000000001110000': 1, '011011000000001111011': 1, '011011000000001111100': 1, '011011000000001111110': 3, '011011100000000000010': 1, '011011100000000010110': 1, '011100000000000001010': 1, '011100000000000111100': 1, '011100000000001000001': 1, '011101000000000000001': 1, '011101000000000000101': 1, '011101000000000001000': 2, '011101000000000001001': 2, '011101000000000001011': 1, '011101000000000001100': 2, '011101000000000001110': 1, '011101000000000010000': 1, '011101000000000010011': 1, '011101000000000010100': 2, '011101000000000010111': 1, '011101000000000011010': 1, '011101000000000100000': 1, '011101000000000100001': 1, '011101000000000100010': 1, '011101000000000100011': 1, '011101000000000101000': 1, '011101000000000101001': 2, '011101000000000101110': 1, '011101000000000101111': 1, '011101000000000110001': 1, '011101000000000110010': 1, '011101000000000110101': 1, '011101000000000110111': 1, '011101000000000111000': 1, '011101000000000111011': 1, '011101000000001000000': 2, '011101000000001000010': 1, '011101000000001000011': 1, '011101000000001000111': 2, '011101000000001001010': 1, '011101000000001010000': 1, '011101000000001010011': 1, '011101000000001010101': 1, '011101000000001011101': 1, '011101000000001100000': 1, '011101000000001100001': 2, '011101000000001100110': 2, '011101000000001101000': 2, '011101000000001101011': 2, '011101000000001101110': 2, '011101000000001101111': 1, '011101000000001110100': 1, '011101000000001111000': 1, '011101000000001111001': 1, '011101000000001111101': 1, '011101000000001111110': 1, '011101100000000101000': 1, '011101100000000111110': 1, '011110000000000011100': 1, '011111000000000000000': 1, '011111000000000000001': 1, '011111000000000000010': 1, '011111000000000000011': 1, '011111000000000000100': 1, '011111000000000000101': 1, '011111000000000000111': 2, '011111000000000001001': 1, '011111000000000010011': 1, '011111000000000010100': 2, '011111000000000010111': 1, '011111000000000011000': 2, '011111000000000011010': 1, '011111000000000011110': 1, '011111000000000100000': 1, '011111000000000100100': 1, '011111000000000100101': 1, '011111000000000101001': 1, '011111000000000101101': 1, '011111000000000110000': 1, '011111000000000110100': 1, '011111000000000110101': 1, '011111000000000111001': 1, '011111000000000111101': 1, '011111000000000111110': 1, '011111000000001000010': 2, '011111000000001000011': 1, '011111000000001000101': 1, '011111000000001010010': 1, '011111000000001011000': 3, '011111000000001011100': 1, '011111000000001011111': 1, '011111000000001100101': 1, '011111000000001100110': 1, '011111000000001100111': 1, '011111000000001101100': 1, '011111000000001101101': 2, '011111000000001110011': 1, '011111000000001110100': 1, '011111000000001111010': 1, '100011000000001000111': 1, '101001000000000011010': 1, '101001000000000101110': 1, '101001000000001101100': 1, '101011000000000101101': 1, '101101000000001111011': 1, '101111000000000000011': 1, '110001000000001111000': 1, '110011000000000100101': 1, '110011000000000111011': 1, '110011000000001001011': 1, '111011000000001001110': 1, '111111000000000001100': 1}\n", + "Estimated Betti Number: 9.1250\n", + "Measurement counts: {'000000100000000100110': 1, '000000100000001111010': 1, '000001000000000000100': 1, '000001000000000010000': 1, '000001000000000010010': 2, '000001000000000011011': 1, '000001000000000100100': 1, '000001000000000100110': 1, '000001000000000101000': 1, '000001000000000101011': 1, '000001000000000110010': 1, '000001000000000110100': 1, '000001000000000110101': 1, '000001000000000111000': 2, '000001000000000111010': 1, '000001000000001000000': 1, '000001000000001000001': 1, '000001000000001000100': 1, '000001000000001000101': 2, '000001000000001000110': 1, '000001000000001000111': 1, '000001000000001001011': 1, '000001000000001001100': 1, '000001000000001001110': 1, '000001000000001010000': 1, '000001000000001010001': 1, '000001000000001010100': 1, '000001000000001010110': 1, '000001000000001010111': 1, '000001000000001100000': 1, '000001000000001101000': 2, '000001000000001101100': 1, '000001000000001101111': 1, '000001000000001110000': 1, '000001000000001110010': 1, '000001000000001110100': 2, '000001000000001110111': 2, '000001000000001111001': 1, '000001000000001111010': 3, '000001000000001111100': 2, 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'110110000000001000010': 1, '110110000000001001011': 1, '110110000000001100011': 1, '110110000000001101011': 1, '110110000000001111011': 1, '110110000000001111101': 1, '110110100000000000101': 1, '110110100000000000111': 1, '110110100000000001111': 1, '110110100000000010001': 1, '110110100000000010100': 1, '110110100000000010101': 1, '110110100000000010111': 1, '110110100000000101000': 1, '110110100000000110110': 1, '110110100000001000100': 1, '110110100000001001100': 2, '110110100000001001101': 1, '110110100000001010100': 1, '110110100000001011010': 1, '110110100000001100111': 1, '110110100000001110000': 1, '110110100000001111100': 1, '110110100000001111110': 1, '110111000000000001111': 1, '110111000000000010110': 1, '110111000000000011100': 1, '110111000000000100101': 1, '110111000000000110001': 2, '110111000000000110100': 2, '110111000000001000001': 1, '110111000000001000110': 1, '110111000000001010010': 1, '110111000000001010101': 1, '110111000000001011000': 1, '110111000000001100101': 1, '110111000000001101101': 1, '110111000000001110010': 1, '110111000000001110011': 1, '110111000000001110101': 1, '110111000000001111011': 1, '110111100000000001100': 1, '110111100000000001111': 1, '110111100000000010010': 1, '110111100000000101010': 1, '110111100000000110000': 1, '110111100000000110111': 1, '110111100000001010111': 1, '111010000000000100011': 1}\n", + "Estimated Betti Number: 8.1250\n", + "Measurement counts: {'000000000000000000011': 1, '000000000000000001000': 1, '000000000000000010001': 1, '000000000000000011111': 2, '000000000000000110101': 1, '000000000000000111001': 1, '000000000000000111011': 1, '000000000000000111110': 1, '000000000000001000011': 1, '000000000000001000111': 1, '000000000000001001000': 1, '000000000000001010010': 1, '000000000000001010100': 1, '000000000000001011011': 1, '000000000000001110111': 2, '000000100000000110101': 1, '000000100000001111010': 1, '000001000000000000101': 1, '000001000000000000110': 1, 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'111001000000000011010': 1, '111001000000000011100': 1, '111001000000000100111': 1, '111001000000000101011': 1, '111001000000000101100': 1, '111001000000000110010': 1, '111001000000000110011': 1, '111001000000000111101': 1, '111001000000000111110': 1, '111001000000001000110': 1, '111001000000001111010': 1, '111010000000000001010': 1, '111010000000000010011': 1, '111010000000000011110': 1, '111010000000000100111': 1, '111010000000000110010': 2, '111010000000000110011': 1, '111010000000000110111': 1, '111010000000001010000': 1, '111010000000001010011': 1, '111010000000001010100': 1, '111010000000001011010': 1, '111010000000001101110': 1, '111010000000001110111': 2, '111010000000001111110': 1, '111011000000000001001': 1, '111011000000000011000': 1, '111011000000000011100': 1, '111011000000000011101': 1, '111011000000000100011': 1, '111011000000000101011': 1, '111011000000000110100': 1, '111011000000001001100': 1, '111011000000001010010': 1, '111011000000001011011': 1, '111011000000001011101': 1, '111011000000001101011': 1, '111011000000001110000': 1, '111011000000001110010': 1, '111011000000001110101': 1, '111011100000000110001': 1, '111100000000000010010': 1, '111100000000000010011': 1, '111100000000000011111': 1, '111100000000000101010': 1, '111100000000000110011': 1, '111100000000001001010': 1, '111100000000001001110': 1, '111100000000001010001': 1, '111100000000001010110': 1, '111100000000001011010': 1, '111100000000001100010': 1, '111100000000001100011': 1, '111100000000001100101': 1, '111100000000001101010': 1, '111100000000001110001': 2, '111100000000001111011': 2, '111101000000000010101': 1, '111101000000000011110': 1, '111101000000000101110': 2, '111101000000000111101': 1, '111101000000001000001': 1, '111101000000001010100': 2, '111101000000001010110': 1, '111101000000001011101': 1, '111101000000001011110': 1, '111101000000001100010': 1, '111101000000001101100': 1, '111101000000001110111': 1, '111101000000001111000': 1, '111110000000000011100': 2, '111110000000000110010': 1, '111110000000000111101': 1, '111110000000000111111': 1, '111110000000001000110': 2, '111110000000001011010': 1, '111110000000001011011': 1, '111110000000001110010': 1, '111110000000001111011': 1, '111111000000000010010': 1, '111111000000000010101': 1, '111111000000000110111': 1, '111111000000000111011': 2, '111111000000000111101': 1, '111111000000000111110': 2, '111111000000001000111': 1, '111111000000001010010': 1, '111111000000001011100': 1, '111111000000001101000': 1, '111111000000001111001': 1, '111111000000001111010': 1, '111111000000001111110': 1, '111111000000001111111': 1, '111111100000001011111': 1}\n", + "Estimated Betti Number: 4.1250\n", + "Measurement counts: {'000000000000000111000': 1, '000000100000000001111': 1, '000001000000000001000': 1, '000001000000000001001': 2, '000001000000000001100': 2, '000001000000000001101': 2, '000001000000000010101': 1, '000001000000000011000': 1, '000001000000000011011': 1, '000001000000000011111': 2, '000001000000000101001': 1, '000001000000000101011': 2, '000001000000000101100': 1, '000001000000000101101': 1, '000001000000000101111': 1, '000001000000000111000': 1, '000001000000000111001': 3, '000001000000000111100': 1, '000001000000000111101': 1, '000001000000001000101': 1, '000001000000001001000': 1, '000001000000001001001': 1, '000001000000001001011': 1, '000001000000001011010': 1, '000001000000001011100': 1, '000001000000001011111': 2, '000001000000001100001': 1, '000001000000001100101': 1, '000001000000001100110': 1, '000001000000001101010': 2, '000001000000001101110': 2, '000001000000001101111': 1, '000001000000001110000': 1, '000001000000001111000': 1, '000001000000001111001': 2, '000001100000000001011': 1, '000001100000000001111': 1, '000001100000000010100': 1, '000001100000000011001': 1, '000001100000000011100': 1, '000001100000000011110': 2, '000001100000000011111': 2, '000001100000000101000': 1, '000001100000000101001': 1, '000001100000000111000': 1, '000001100000000111010': 1, '000001100000000111011': 2, '000001100000000111100': 1, '000001100000000111111': 1, '000001100000001001100': 1, '000001100000001001101': 2, '000001100000001001110': 1, '000001100000001010011': 1, '000001100000001011100': 1, '000001100000001100001': 1, '000001100000001100011': 1, '000001100000001101011': 1, '000001100000001101101': 1, '000001100000001101111': 1, '000001100000001111001': 1, '000001100000001111011': 1, '000010100000001001001': 1, '000011000000000001000': 1, '000011000000000001010': 1, '000011000000000001011': 1, '000011000000000001100': 1, '000011000000000001111': 1, '000011000000000010001': 1, '000011000000000011000': 2, '000011000000000011001': 1, '000011000000000011110': 1, '000011000000000101001': 1, '000011000000000101011': 1, '000011000000000101100': 2, '000011000000000111000': 2, '000011000000000111110': 1, '000011000000000111111': 1, '000011000000001001000': 1, '000011000000001001001': 1, 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'000011100000001100100': 1, '000011100000001101011': 2, '000011100000001101100': 1, '000011100000001101111': 1, '000011100000001110100': 1, '000011100000001111010': 2, '000011100000001111011': 1, '000011100000001111100': 1, '000011100000001111101': 1, '000100000000000000010': 1, '000100000000000010110': 1, '000100000000000110010': 1, '000100100000000111001': 1, '000100100000001001111': 1, '000100100000001101001': 1, '000101000000000000010': 1, '000101000000000001000': 2, '000101000000000001001': 2, '000101000000000001100': 2, '000101000000000001101': 5, '000101000000000001110': 2, '000101000000000001111': 1, '000101000000000010110': 1, '000101000000000011000': 1, '000101000000000011001': 1, '000101000000000011011': 1, '000101000000000011110': 1, '000101000000000100111': 1, '000101000000000101000': 2, '000101000000000101001': 1, '000101000000000101010': 1, '000101000000000101011': 3, '000101000000000101101': 1, '000101000000000101110': 2, '000101000000000101111': 1, 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'000101100000000001001': 1, '000101100000000001010': 2, '000101100000000001100': 1, '000101100000000001110': 1, '000101100000000001111': 3, '000101100000000010000': 1, '000101100000000010110': 1, '000101100000000011001': 2, '000101100000000011010': 1, '000101100000000011011': 3, '000101100000000011100': 1, '000101100000000011110': 2, '000101100000000100110': 1, '000101100000000101000': 1, '000101100000000101001': 1, '000101100000000101010': 2, '000101100000000101100': 3, '000101100000000101110': 1, '000101100000000110010': 1, '000101100000000111000': 2, '000101100000000111001': 1, '000101100000000111010': 1, '000101100000000111011': 1, '000101100000000111100': 3, '000101100000000111101': 2, '000101100000000111110': 2, '000101100000000111111': 2, '000101100000001001000': 1, '000101100000001001010': 4, '000101100000001001011': 1, '000101100000001001100': 2, '000101100000001001111': 1, '000101100000001010001': 1, '000101100000001011000': 2, '000101100000001011001': 1, '000101100000001011010': 1, '000101100000001011100': 1, '000101100000001011101': 2, '000101100000001011110': 1, '000101100000001100100': 1, '000101100000001101000': 1, '000101100000001101001': 4, '000101100000001101011': 2, '000101100000001101100': 1, '000101100000001101101': 2, '000101100000001110110': 1, '000101100000001111000': 2, '000101100000001111001': 2, '000101100000001111100': 2, '000101100000001111101': 2, '000101100000001111110': 1, '000110000000000011000': 1, '000110000000000100001': 1, '000110000000000100111': 1, '000110000000001011011': 1, '000110100000000001010': 1, '000110100000001001101': 1, '000110100000001101011': 1, '000110100000001111101': 2, '000111000000000001000': 2, '000111000000000001001': 1, '000111000000000001010': 1, '000111000000000001011': 1, '000111000000000001100': 1, '000111000000000001101': 1, '000111000000000001110': 1, '000111000000000011010': 1, '000111000000000011011': 1, '000111000000000011100': 1, '000111000000000011101': 2, 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'001001000000000001101': 3, '001001000000000001110': 1, '001001000000000011001': 3, '001001000000000011011': 1, '001001000000000011100': 1, '001001000000000100001': 1, '001001000000000100011': 1, '001001000000000101100': 2, '001001000000000101110': 1, '001001000000000111000': 1, '001001000000000111001': 1, '001001000000000111010': 1, '001001000000001001000': 1, '001001000000001001101': 1, '001001000000001001110': 1, '001001000000001001111': 1, '001001000000001010011': 1, '001001000000001010100': 1, '001001000000001010111': 1, '001001000000001011001': 1, '001001000000001011100': 1, '001001000000001011111': 1, '001001000000001101000': 1, '001001000000001101010': 1, '001001000000001101011': 1, '001001000000001101100': 1, '001001000000001101101': 1, '001001000000001101111': 1, '001001000000001111000': 1, '001001000000001111001': 1, '001001000000001111010': 1, '001001000000001111100': 1, '001001000000001111101': 1, '001001000000001111110': 1, '001001100000000000110': 1, 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'001011000000000001000': 2, '001011000000000001101': 1, '001011000000000010011': 1, '001011000000000101011': 1, '001011000000000110111': 1, '001011000000000111000': 4, '001011000000000111010': 1, '001011000000000111100': 1, '001011000000001001000': 1, '001011000000001001001': 1, '001011000000001001010': 3, '001011000000001001101': 1, '001011000000001011000': 1, '001011000000001011001': 1, '001011000000001011101': 1, '001011000000001011111': 1, '001011000000001100101': 1, '001011000000001101000': 1, '001011000000001101011': 1, '001011000000001101100': 1, '001011000000001111000': 1, '001011000000001111010': 2, '001011000000001111111': 1, '001011100000000001111': 2, '001011100000000010101': 1, '001011100000000011100': 1, '001011100000000011110': 1, '001011100000000101001': 1, '001011100000000101010': 1, '001011100000000101011': 1, '001011100000000111001': 1, '001011100000000111010': 1, '001011100000000111100': 1, '001011100000000111110': 3, '001011100000001001011': 1, '001011100000001001110': 1, '001011100000001001111': 1, '001011100000001011000': 1, '001011100000001011001': 1, '001011100000001011010': 1, '001011100000001011011': 1, '001011100000001011100': 1, '001011100000001101010': 1, '001011100000001101100': 1, '001011100000001101111': 1, '001011100000001111000': 1, '001011100000001111001': 2, '001011100000001111011': 2, '001011100000001111100': 1, '001011100000001111101': 1, '001100000000000001000': 1, '001100000000001001000': 1, '001100100000000110010': 1, '001100100000001001001': 1, '001100100000001101011': 1, '001101000000000000000': 1, '001101000000000001000': 1, '001101000000000001010': 2, '001101000000000001100': 1, '001101000000000001101': 1, '001101000000000001110': 1, '001101000000000010001': 1, '001101000000000011010': 2, '001101000000000011100': 3, '001101000000000011101': 1, '001101000000000011110': 1, '001101000000000011111': 2, '001101000000000100010': 1, '001101000000000101001': 1, '001101000000000101010': 4, 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'011001000000000110110': 1, '011001000000001011100': 1, '011001100000001001000': 1, '011011000000000001100': 1, '011011000000001001110': 1, '011011100000000001001': 1, '011101100000001111001': 1, '011101100000001111100': 1, '011111000000000101001': 1, '011111000000000110010': 1, '011111100000000011101': 1, '011111100000001001010': 1, '100001000000001111000': 1, '100001100000000001000': 1, '100011100000001111010': 1, '100101000000000001000': 1, '100101100000001001100': 1, '100111000000000101000': 1, '100111000000000101001': 1, '100111100000000001111': 1, '101001100000000000101': 1, '101101000000000011011': 1, '101101000000001111010': 1, '101101100000000111111': 1, '101111000000001011100': 1, '101111100000000101000': 1}\n", + "Estimated Betti Number: 9.5000\n", + "Measurement counts: {'000000000000000001000': 1, '000000000000000001001': 1, '000000000000000010000': 1, '000000000000000101000': 1, '000000000000000101010': 1, '000000000000000110001': 1, '000000000000000110110': 1, 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'000111100000000001101': 1, '000111100000000001110': 1, '000111100000000001111': 1, '000111100000000010000': 1, '000111100000000010001': 1, '000111100000000010100': 1, '000111100000000011000': 1, '000111100000000011101': 1, '000111100000000100001': 1, '000111100000000101000': 1, '000111100000000101001': 1, '000111100000000101011': 1, '000111100000000101101': 3, '000111100000000101110': 2, '000111100000000110010': 2, '000111100000000110101': 1, '000111100000000110111': 2, '000111100000000111000': 1, '000111100000000111010': 1, '000111100000000111011': 1, '000111100000000111100': 1, '000111100000000111110': 1, '000111100000001000011': 1, '000111100000001000100': 1, '000111100000001001001': 2, '000111100000001001100': 1, '000111100000001001111': 1, '000111100000001010111': 2, '000111100000001011000': 1, '000111100000001011001': 1, '000111100000001011100': 1, '000111100000001011110': 1, '000111100000001100001': 1, '000111100000001100010': 1, '000111100000001100100': 3, '000111100000001101001': 1, '000111100000001101010': 2, '000111100000001110100': 1, '000111100000001110101': 1, '000111100000001111001': 2, '000111100000001111100': 2, '000111100000001111101': 1, '000111100000001111110': 1, '000111100000001111111': 2, '001001100000000001010': 2, '001001100000000100101': 1, '001010100000001111110': 1, '001011100000000101101': 1, '001100100000000101110': 1, '001101100000000100011': 1, '001110000000001011001': 1, '001110100000001101010': 1, '001110100000001111100': 1, '001111100000000111000': 1, '010000000000000001101': 1, '010000100000001110111': 1, '010001000000000111011': 1, '010001000000001000101': 1, '010001000000001011110': 1, '010001100000001111010': 1, '010010000000000011111': 1, '010010100000000110110': 1, '010010100000001100000': 1, '010011000000000111000': 1, '010011000000000111111': 1, '010011000000001111001': 1, '010011100000000111011': 1, '010100100000000101001': 1, '010101000000001001101': 1, '010110100000000011001': 1, '010110100000000100100': 1, '010110100000000101000': 1, '010111000000000000000': 1, '010111100000000110101': 1, '010111100000001111101': 1, '100000100000000010101': 1, '100000100000000101011': 1, '100001000000000000100': 1, '100001000000000001001': 1, '100001000000000011100': 1, '100001000000001010011': 1, '100001100000000001010': 1, '100001100000000100010': 1, '100010100000000001000': 1, '100010100000000001111': 1, '100010100000001111111': 1, '100011100000001101001': 1, '100110000000001101000': 1, '100111000000001001001': 1, '100111100000001001010': 1, '110010000000001011001': 1}\n", + "Estimated Betti Number: 31.3750\n", + "Measurement counts: {'000000100000001010010': 1, '000001000000000100111': 1, '000001100000000100101': 1, '000001100000000110000': 1, '000001100000001110110': 1, '000011100000000011000': 1, '000011100000001001100': 1, '000100000000001101001': 1, '000100100000000011101': 1, '000101000000000111101': 1, '000101000000001011011': 1, '000101000000001101110': 1, 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'111111100000001010100': 1, '111111100000001011101': 1}\n", + "Estimated Betti Number: 0.6250\n", + "Measurement counts: {'000000000000000001010': 1, '000000000000000011101': 1, '000000000000000111100': 1, '000000000000001001100': 1, '000000000000001011000': 1, '000000000000001100000': 1, '000000000000001110010': 1, '000000000000001110110': 1, '000000000000001111111': 1, '000000100000000000010': 1, '000000100000000001001': 1, '000000100000001011010': 1, '000000100000001011110': 1, '000000100000001100010': 2, '000000100000001110010': 1, '000001000000000110001': 1, '000001000000000110100': 1, '000001000000000111011': 1, '000001000000001010001': 1, '000001000000001010111': 2, '000001000000001011000': 1, '000001000000001011010': 1, '000001000000001100101': 1, '000001000000001101001': 1, '000001000000001110101': 1, '000001000000001111011': 2, '000001100000000001010': 1, '000001100000000011010': 1, '000001100000000011100': 1, '000001100000000101111': 1, '000001100000000110011': 1, 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'111110100000001110100': 1, '111110100000001111001': 1}\n", + "Estimated Betti Number: 5.0000\n", + "Measurement counts: {'000000000000000000101': 1, '000000000000000000110': 1, '000000000000000000111': 2, '000000000000000010000': 1, '000000000000000010001': 1, '000000000000000010110': 1, '000000000000000011000': 1, '000000000000000011010': 1, '000000000000000101100': 1, '000000000000000110001': 1, '000000000000000110110': 1, '000000000000001000000': 1, '000000000000001000010': 2, '000000000000001001010': 1, '000000000000001010111': 1, '000000000000001101100': 1, '000000000000001101111': 1, '000001000000000010000': 1, '000001000000000010010': 1, '000001000000000010111': 1, '000001000000000011000': 1, '000001000000000100010': 1, '000001000000000100110': 1, '000001000000000111001': 1, '000001000000000111011': 1, '000001000000000111111': 1, '000001000000001000111': 1, '000001000000001001100': 1, '000001000000001010010': 1, '000001000000001010111': 1, '000001000000001011100': 1, 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'111111000000001000010': 2, '111111000000001000100': 1, '111111000000001000110': 1, '111111000000001010010': 2}\n", + "Estimated Betti Number: 4.3750\n", + "Measurement counts: {'000000000000000001110': 1, '000000100000000000011': 1, '000000100000000000100': 1, '000000100000000000110': 1, '000000100000000000111': 1, '000000100000000001001': 1, '000000100000000001101': 1, '000000100000000001111': 4, '000000100000000010000': 1, '000000100000000010001': 1, '000000100000000010010': 1, '000000100000000010110': 1, '000000100000000011001': 1, '000000100000000011110': 1, '000000100000000011111': 1, '000000100000000100000': 2, '000000100000000100010': 2, '000000100000000100101': 1, '000000100000000101101': 1, '000000100000000101110': 1, '000000100000000101111': 1, '000000100000000110100': 1, '000000100000000110101': 2, '000000100000000110110': 2, '000000100000000111001': 2, '000000100000000111100': 1, '000000100000000111101': 1, '000000100000001000001': 2, '000000100000001000010': 1, 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'111101100000001001001': 1, '111101100000001100001': 1, '111110000000000000000': 1, '111110000000000000011': 1, '111110000000000001110': 1, '111110000000000101000': 1, '111110000000000110100': 1, '111110000000001001001': 1, '111110000000001010001': 1, '111110000000001011001': 1, '111110000000001100100': 1, '111110000000001110111': 1, '111110000000001111010': 1, '111110100000000100001': 1, '111110100000000100010': 1, '111110100000000101001': 1, '111110100000001000011': 1, '111110100000001010000': 1, '111110100000001100001': 1, '111110100000001111000': 1, '111111000000000001001': 1, '111111000000000010011': 1, '111111000000000011000': 1, '111111000000000100001': 1, '111111000000000100111': 1, '111111000000000111001': 1, '111111000000001000000': 1, '111111100000000000000': 1, '111111100000000001101': 1, '111111100000000010010': 1, '111111100000000101100': 1, '111111100000001110101': 1, '111111100000001111001': 1}\n", + "Estimated Betti Number: 4.6250\n", + "Measurement counts: 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'100010000000000000000': 1, '100010100000000011100': 1, '100011000000001110001': 1, '100011000000001110101': 1, '100011000000001111111': 1, '101010000000001111010': 1, '110000100000000011100': 1, '110000100000000111001': 1, '110001100000001010000': 1, '110001100000001111110': 1, '110010000000001111010': 1, '110010000000001111101': 1, '110011000000000110011': 1, '110011000000000111101': 1}\n", + "Estimated Betti Number: 35.0000\n", + "Measurement counts: {'000000000000000000100': 1, '000000000000000100100': 1, '000000000000000101000': 1, '000000000000000110001': 1, '000000000000000110111': 1, '000000000000000111000': 1, '000000000000000111011': 1, '000000000000000111101': 1, '000000000000001000100': 1, '000000000000001001010': 1, '000000000000001010011': 1, '000000000000001011010': 1, '000000000000001100001': 1, '000000000000001110001': 1, '000000000000001110111': 1, '000000000000001111111': 1, '000001000000000011000': 1, '000001000000000011011': 1, '000001000000000100011': 1, 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'110110000000000110110': 1, '110111000000001010000': 1, '111001000000000111100': 1, '111101000000000000111': 1, '111101000000000101010': 1}\n", + "Estimated Betti Number: 4.3750\n", + "Measurement counts: {'000000000000000001000': 1, '000000000000000010101': 1, '000000000000000110000': 1, '000000000000001011011': 1, '000000100000000110011': 1, '000000100000000111001': 1, '000000100000000111010': 1, '000000100000001001001': 1, '000000100000001111000': 1, '000010000000000001011': 1, '000010000000000001110': 1, '000010000000000001111': 1, '000010000000000011011': 1, '000010000000000100001': 1, '000010000000000110000': 1, '000010000000000110011': 1, '000010000000000110110': 1, '000010000000001000010': 2, '000010000000001000110': 1, '000010000000001000111': 1, '000010000000001001000': 1, '000010000000001001010': 1, '000010000000001001100': 1, '000010000000001010000': 1, '000010000000001010101': 1, '000010000000001011000': 2, '000010000000001011010': 1, '000010000000001100110': 1, 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'000011000000000111001': 1, '000011100000000000010': 1, '000011100000000001110': 1, '000100000000000100000': 1, '000100000000001000000': 1, '000100100000000100001': 1, '000100100000000111011': 1, '000100100000000111110': 1, '000100100000001011100': 1, '000100100000001101111': 1, '000110000000000000000': 1, '000110000000000000001': 1, '000110000000000000100': 1, '000110000000000001000': 1, '000110000000000001010': 1, '000110000000000001111': 1, '000110000000000010000': 1, '000110000000000011000': 1, '000110000000000100101': 1, '000110000000000100110': 1, '000110000000001000010': 2, '000110000000001000100': 1, '000110000000001000111': 1, '000110000000001001011': 2, '000110000000001001100': 1, '000110000000001010000': 1, '000110000000001010001': 1, '000110000000001010100': 2, '000110000000001010101': 1, '000110000000001011100': 1, '000110000000001011101': 2, '000110000000001100100': 2, '000110000000001100110': 1, '000110000000001101101': 2, '000110000000001111101': 1, '000110000000001111110': 1, '000110100000000000011': 1, '000110100000000001010': 1, '000110100000000010001': 1, '000110100000000010011': 2, '000110100000000011000': 1, '000110100000000011010': 1, '000110100000000011110': 1, '000110100000000100100': 1, '000110100000000101001': 3, '000110100000000101010': 3, '000110100000000101011': 1, '000110100000000110000': 2, '000110100000000110001': 1, '000110100000000111001': 1, '000110100000000111011': 1, '000110100000000111100': 1, '000110100000001000001': 2, '000110100000001000010': 3, '000110100000001000101': 1, '000110100000001000110': 2, '000110100000001000111': 1, '000110100000001001001': 1, '000110100000001001011': 1, '000110100000001001110': 1, '000110100000001010010': 2, '000110100000001010011': 1, '000110100000001010100': 1, '000110100000001011000': 1, '000110100000001100111': 1, '000110100000001101100': 2, '000110100000001110001': 1, '000110100000001110101': 1, '000110100000001111001': 1, '000111000000000100011': 1, 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'001010000000001011011': 1, '001010000000001100011': 1, '001010000000001100100': 1, '001010000000001100101': 1, '001010000000001101000': 1, '001010000000001110000': 1, '001010000000001110101': 1, '001010000000001111001': 1, '001010000000001111111': 1, '001010100000000000011': 1, '001010100000000000100': 1, '001010100000000000101': 1, '001010100000000001000': 2, '001010100000000001011': 1, '001010100000000010000': 2, '001010100000000010010': 1, '001010100000000010011': 2, '001010100000000010111': 1, '001010100000000011101': 1, '001010100000000100100': 2, '001010100000000100111': 1, '001010100000000101010': 1, '001010100000000101100': 1, '001010100000000101110': 1, '001010100000000101111': 1, '001010100000000110000': 1, '001010100000000110001': 1, '001010100000000110010': 2, '001010100000000110110': 1, '001010100000000111100': 2, '001010100000000111110': 1, '001010100000001000001': 1, '001010100000001000010': 1, '001010100000001000110': 1, '001010100000001001000': 1, '001010100000001001100': 1, '001010100000001001110': 1, '001010100000001010000': 2, '001010100000001010001': 1, '001010100000001010011': 1, '001010100000001010100': 1, '001010100000001010101': 1, '001010100000001011001': 1, '001010100000001011011': 1, '001010100000001011100': 1, '001010100000001011101': 1, '001010100000001100100': 1, '001010100000001101111': 1, '001010100000001110000': 1, '001010100000001110001': 1, '001011000000000000010': 1, '001011000000001000101': 1, '001011100000000101010': 1, '001011100000001110000': 1, '001100000000000110001': 1, '001100000000000110101': 1, '001100000000001000111': 1, '001100000000001110001': 1, '001100100000000000101': 1, '001100100000001001111': 1, '001110000000000000101': 1, '001110000000000001001': 1, '001110000000000001010': 1, '001110000000000001100': 1, '001110000000000001101': 1, '001110000000000001111': 2, '001110000000000010100': 1, '001110000000000011000': 1, '001110000000000011001': 1, '001110000000000011101': 1, 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'001110100000000011100': 1, '001110100000000100000': 1, '001110100000000100010': 1, '001110100000000100101': 1, '001110100000000101001': 1, '001110100000000101010': 2, '001110100000000101101': 1, '001110100000000110000': 1, '001110100000000110110': 2, '001110100000000111110': 1, '001110100000001000000': 1, '001110100000001000001': 2, '001110100000001000011': 1, '001110100000001000100': 1, '001110100000001001010': 2, '001110100000001001011': 1, '001110100000001001111': 1, '001110100000001010111': 1, '001110100000001011101': 1, '001110100000001100010': 1, '001110100000001100110': 1, '001110100000001101101': 1, '001110100000001110110': 1, '001110100000001111000': 1, '001110100000001111110': 1, '001111000000000111000': 1, '001111100000001011001': 1, '010010000000000110100': 1, '010010100000001000010': 1, '010110000000000010101': 1, '010110000000001001010': 1, '010110000000001100101': 1, '010110100000001101011': 1, '011010000000000010110': 1, '100000000000000000110': 1, '100000000000000001101': 1, '100000000000000010000': 1, '100000000000000010010': 1, '100000000000000110001': 1, '100000000000001000001': 1, '100000000000001001111': 1, '100000000000001011100': 1, '100000000000001110001': 1, '100000100000000001111': 1, '100000100000000010111': 1, '100000100000000110001': 1, '100000100000001001111': 1, '100001100000000010101': 1, '100010000000000000001': 3, '100010000000000000010': 3, '100010000000000000101': 2, '100010000000000000111': 1, '100010000000000001011': 1, '100010000000000001100': 1, '100010000000000001101': 2, '100010000000000001110': 2, '100010000000000001111': 2, '100010000000000010000': 1, '100010000000000010001': 2, '100010000000000010011': 1, '100010000000000010100': 1, '100010000000000010110': 1, '100010000000000011001': 1, '100010000000000011010': 1, '100010000000000100001': 1, '100010000000000100100': 1, '100010000000000100101': 1, '100010000000000100111': 1, '100010000000000101000': 1, '100010000000000101001': 1, '100010000000000101010': 3, '100010000000000101011': 1, '100010000000000101100': 1, '100010000000000101101': 2, '100010000000000101110': 1, '100010000000000101111': 1, '100010000000000110000': 2, '100010000000000110010': 1, '100010000000000110011': 1, '100010000000000110101': 1, '100010000000000110110': 1, '100010000000000111000': 1, '100010000000000111001': 1, '100010000000000111010': 1, '100010000000000111100': 2, '100010000000000111101': 1, '100010000000000111111': 1, '100010000000001000001': 1, '100010000000001000010': 3, '100010000000001000011': 1, '100010000000001000100': 1, '100010000000001000111': 1, '100010000000001001000': 1, '100010000000001001100': 1, '100010000000001001111': 1, '100010000000001010000': 4, '100010000000001010001': 1, '100010000000001010010': 1, '100010000000001010101': 1, '100010000000001010111': 2, '100010000000001011001': 2, '100010000000001011010': 1, '100010000000001011011': 1, '100010000000001011100': 1, '100010000000001100000': 1, '100010000000001100101': 1, '100010000000001100110': 1, '100010000000001100111': 1, '100010000000001101000': 1, '100010000000001101001': 1, '100010000000001101011': 1, '100010000000001101100': 1, '100010000000001101110': 1, '100010000000001110000': 1, '100010000000001110001': 2, '100010000000001110100': 1, '100010000000001110111': 1, '100010100000000000010': 1, '100010100000000000100': 2, '100010100000000001000': 1, '100010100000000001101': 2, '100010100000000010000': 1, '100010100000000010001': 2, '100010100000000010010': 1, '100010100000000011001': 1, '100010100000000011101': 1, '100010100000000011110': 2, '100010100000000100001': 3, '100010100000000100100': 1, '100010100000000100101': 2, '100010100000000100111': 1, '100010100000000101010': 1, '100010100000000101011': 2, '100010100000000101100': 1, '100010100000000101110': 1, '100010100000000101111': 1, '100010100000000110000': 2, '100010100000000110001': 1, '100010100000000110011': 2, '100010100000000111000': 2, '100010100000000111101': 1, '100010100000001000010': 2, '100010100000001000101': 1, '100010100000001001000': 1, '100010100000001001001': 1, '100010100000001001011': 1, '100010100000001001100': 2, '100010100000001001110': 1, '100010100000001001111': 2, '100010100000001010001': 1, '100010100000001010011': 1, '100010100000001010100': 1, '100010100000001010110': 2, '100010100000001010111': 1, '100010100000001011000': 1, '100010100000001011001': 1, '100010100000001011100': 2, '100010100000001011101': 1, '100010100000001100100': 1, '100010100000001100101': 1, '100010100000001101000': 1, '100010100000001101011': 1, '100010100000001101111': 1, '100010100000001110010': 2, '100010100000001110110': 2, '100010100000001111001': 2, '100010100000001111100': 1, '100010100000001111101': 1, '100010100000001111110': 2, '100011000000000100011': 1, '100011000000001011011': 1, '100011000000001111010': 1, '100011100000001010000': 1, '100011100000001101111': 1, '100100000000000000111': 1, '100100000000000010101': 1, '100100000000001001011': 1, '100100000000001011011': 1, '100100000000001011111': 1, '100100100000000000011': 1, '100100100000000001011': 1, '100100100000000010010': 1, '100100100000000010111': 1, '100100100000000011000': 1, '100100100000001001010': 1, '100100100000001101010': 2, '100110000000000000000': 1, '100110000000000000111': 1, '100110000000000001000': 1, '100110000000000001010': 1, '100110000000000001101': 2, '100110000000000001111': 1, '100110000000000010010': 1, '100110000000000010100': 1, '100110000000000011001': 2, '100110000000000011010': 1, '100110000000000011111': 1, '100110000000000100000': 1, '100110000000000100001': 1, '100110000000000100110': 2, '100110000000000101011': 1, '100110000000000101100': 1, '100110000000000110001': 1, '100110000000000110010': 1, '100110000000000110110': 2, '100110000000000110111': 2, '100110000000000111101': 1, '100110000000001000011': 1, '100110000000001000100': 1, '100110000000001000101': 2, '100110000000001000110': 2, '100110000000001000111': 1, '100110000000001001001': 2, '100110000000001001010': 1, '100110000000001001011': 1, '100110000000001001110': 1, '100110000000001010000': 1, '100110000000001010010': 2, '100110000000001010100': 1, '100110000000001010110': 1, '100110000000001011101': 1, '100110000000001011110': 2, '100110000000001011111': 2, '100110000000001100101': 1, '100110000000001100110': 1, '100110000000001100111': 1, '100110000000001101001': 1, '100110000000001101011': 1, '100110000000001101100': 1, '100110000000001101111': 2, '100110000000001110000': 1, '100110000000001110001': 1, '100110000000001110010': 1, '100110000000001110011': 3, '100110000000001110101': 1, '100110000000001110110': 1, '100110000000001110111': 1, '100110000000001111011': 1, '100110000000001111111': 1, '100110100000000000011': 3, '100110100000000000100': 1, '100110100000000000111': 1, '100110100000000001000': 1, '100110100000000001010': 1, '100110100000000001111': 1, '100110100000000010010': 1, '100110100000000010100': 1, '100110100000000010110': 3, '100110100000000011101': 1, '100110100000000100111': 1, '100110100000000101000': 2, '100110100000000101001': 1, '100110100000000101011': 2, '100110100000000101100': 1, '100110100000000101110': 1, '100110100000000101111': 2, '100110100000000110000': 1, '100110100000000110001': 2, '100110100000000110010': 1, '100110100000000110011': 1, '100110100000000110101': 1, '100110100000000110111': 1, '100110100000000111010': 1, '100110100000000111111': 2, '100110100000001000000': 1, '100110100000001000011': 1, '100110100000001000110': 2, '100110100000001001001': 1, '100110100000001001010': 2, '100110100000001001011': 2, '100110100000001001101': 1, '100110100000001001111': 1, '100110100000001010000': 1, '100110100000001010001': 1, '100110100000001010011': 1, '100110100000001010100': 4, '100110100000001010101': 2, '100110100000001010110': 2, '100110100000001011000': 2, '100110100000001011001': 1, '100110100000001011010': 3, '100110100000001100010': 1, '100110100000001101000': 1, '100110100000001101010': 1, '100110100000001101101': 1, '100110100000001101110': 1, '100110100000001101111': 1, '100110100000001110000': 1, '100110100000001110011': 2, '100110100000001110110': 1, '100110100000001111000': 2, '100110100000001111001': 1, '100110100000001111010': 1, '100110100000001111011': 1, '100110100000001111100': 1, '100110100000001111101': 1, '100111000000001000100': 1, '100111100000000100100': 1, '101000000000000111011': 1, '101000000000001011010': 1, '101000000000001100011': 1, '101000000000001100101': 1, '101000000000001101000': 1, '101000100000000101101': 1, '101000100000001011010': 1, '101010000000000000001': 1, '101010000000000000010': 1, '101010000000000000100': 2, '101010000000000000110': 3, '101010000000000001001': 1, '101010000000000001010': 1, '101010000000000010000': 1, '101010000000000010001': 2, '101010000000000010011': 1, '101010000000000010110': 2, '101010000000000010111': 1, '101010000000000011001': 2, '101010000000000011100': 1, '101010000000000100010': 1, '101010000000000100101': 2, '101010000000000100110': 1, '101010000000000101000': 1, '101010000000000101001': 1, '101010000000000101101': 1, '101010000000000101110': 1, '101010000000000110011': 2, '101010000000000110111': 1, '101010000000000111000': 2, '101010000000000111001': 1, '101010000000000111010': 2, '101010000000000111011': 2, '101010000000000111101': 2, '101010000000001000000': 1, '101010000000001000001': 1, '101010000000001000011': 1, '101010000000001000100': 1, '101010000000001000111': 1, '101010000000001001000': 3, '101010000000001001001': 1, '101010000000001001010': 2, '101010000000001001011': 3, '101010000000001001101': 1, '101010000000001001110': 1, '101010000000001001111': 1, '101010000000001010000': 2, '101010000000001010010': 1, '101010000000001010101': 1, '101010000000001010110': 2, '101010000000001010111': 1, '101010000000001011001': 1, '101010000000001011010': 2, '101010000000001011100': 3, '101010000000001011101': 3, '101010000000001011110': 1, '101010000000001011111': 1, '101010000000001100000': 1, '101010000000001100011': 2, '101010000000001100101': 1, '101010000000001101110': 1, '101010000000001101111': 1, '101010000000001110000': 1, '101010000000001110010': 1, '101010000000001110011': 1, '101010000000001110100': 2, '101010000000001110110': 1, '101010000000001110111': 1, '101010000000001111010': 1, '101010100000000000010': 1, '101010100000000000011': 1, '101010100000000000100': 2, '101010100000000000110': 2, '101010100000000001001': 2, '101010100000000001100': 1, '101010100000000010000': 1, '101010100000000010001': 2, '101010100000000010011': 1, '101010100000000010101': 1, '101010100000000010110': 1, '101010100000000011001': 1, '101010100000000011010': 2, '101010100000000011101': 1, '101010100000000011110': 1, '101010100000000011111': 1, '101010100000000100000': 1, '101010100000000100010': 1, '101010100000000100011': 1, '101010100000000100100': 1, '101010100000000100101': 1, '101010100000000101000': 1, '101010100000000101001': 1, '101010100000000101100': 1, '101010100000000101101': 1, '101010100000000110010': 2, '101010100000000110100': 1, '101010100000000110101': 1, '101010100000000111100': 2, '101010100000000111110': 1, '101010100000000111111': 1, '101010100000001000000': 3, '101010100000001000010': 1, '101010100000001000101': 1, '101010100000001000110': 2, '101010100000001000111': 3, '101010100000001001010': 2, '101010100000001001011': 1, '101010100000001001100': 2, '101010100000001001110': 1, '101010100000001001111': 1, '101010100000001010000': 1, '101010100000001010001': 1, '101010100000001010010': 2, '101010100000001010011': 1, '101010100000001010110': 1, '101010100000001011000': 1, '101010100000001011010': 1, '101010100000001011100': 1, '101010100000001011101': 1, '101010100000001011111': 1, '101010100000001100001': 1, '101010100000001101000': 1, '101010100000001101001': 1, '101010100000001101010': 1, '101010100000001101111': 2, '101010100000001110000': 2, '101010100000001111011': 1, '101010100000001111101': 1, '101011000000001011101': 1, '101011100000000100101': 1, '101011100000000110011': 1, '101100000000000000011': 1, '101100000000000000110': 1, '101100000000000000111': 1, '101100000000000100110': 1, '101100000000000101011': 1, '101100000000000110101': 1, '101100000000000111100': 1, '101100000000001001101': 1, '101100000000001101011': 1, '101100000000001110010': 1, '101100000000001110100': 1, '101100100000000000001': 1, '101100100000000010000': 1, '101100100000000010011': 1, '101100100000000011000': 1, '101100100000000011010': 1, '101100100000000100000': 1, '101100100000000100100': 1, '101100100000001010001': 1, '101100100000001010110': 1, '101100100000001011111': 1, '101100100000001100010': 1, '101110000000000000010': 1, '101110000000000000100': 1, '101110000000000000110': 1, '101110000000000001000': 1, '101110000000000001001': 3, '101110000000000001011': 1, '101110000000000010000': 3, '101110000000000010010': 1, '101110000000000010111': 2, '101110000000000011010': 1, '101110000000000100000': 1, '101110000000000100100': 1, '101110000000000100101': 3, '101110000000000110010': 2, '101110000000000111001': 2, '101110000000000111010': 1, '101110000000000111100': 1, '101110000000001000001': 1, '101110000000001000010': 1, '101110000000001000011': 2, '101110000000001000100': 1, '101110000000001000111': 1, '101110000000001001100': 2, '101110000000001001101': 1, '101110000000001001110': 2, '101110000000001010001': 1, '101110000000001010010': 1, '101110000000001010101': 2, '101110000000001011111': 1, '101110000000001100000': 1, '101110000000001100001': 1, '101110000000001100101': 1, '101110000000001101011': 1, '101110000000001101101': 1, '101110000000001101111': 1, '101110000000001110010': 1, '101110000000001110011': 1, '101110000000001110111': 1, '101110000000001111100': 1, '101110100000000000001': 1, '101110100000000000100': 1, '101110100000000000101': 1, '101110100000000001001': 1, '101110100000000001110': 1, '101110100000000001111': 1, '101110100000000010000': 1, '101110100000000010001': 1, '101110100000000010110': 1, '101110100000000011000': 1, '101110100000000011010': 1, '101110100000000011011': 2, '101110100000000011111': 1, '101110100000000100000': 1, '101110100000000100001': 1, '101110100000000100010': 1, '101110100000000100011': 1, '101110100000000100110': 1, '101110100000000100111': 1, '101110100000000101000': 2, '101110100000000101001': 1, '101110100000000101010': 1, '101110100000000101100': 1, '101110100000000101111': 1, '101110100000000111010': 1, '101110100000000111011': 1, '101110100000000111101': 1, '101110100000001000000': 1, '101110100000001000001': 2, '101110100000001000010': 4, '101110100000001000011': 2, '101110100000001000100': 1, '101110100000001000110': 1, '101110100000001000111': 2, '101110100000001001011': 2, '101110100000001001100': 1, '101110100000001001101': 4, '101110100000001001110': 2, '101110100000001001111': 1, '101110100000001010000': 1, '101110100000001010100': 1, '101110100000001011000': 2, '101110100000001011010': 1, '101110100000001011011': 3, '101110100000001011101': 2, '101110100000001011111': 1, '101110100000001100000': 1, '101110100000001101000': 1, '101110100000001101010': 1, '101110100000001101100': 1, '101110100000001101101': 1, '101110100000001101111': 1, '101110100000001110010': 1, '101110100000001110101': 1, '101110100000001110111': 1, '101110100000001111000': 1, '101110100000001111100': 2, '101111000000001011010': 1, '101111000000001100011': 1, '110110100000000101111': 1, '110110100000001011110': 1, '111010000000000111011': 1, '111111000000001000101': 1}\n", + "Estimated Betti Number: 1.1250\n", + "Measurement counts: {'000001000000001010100': 1, '000001000000001011110': 1, '000001000000001101111': 1, '000010100000000110101': 1, '000010100000001100011': 1, 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Betti Number: 7.5000\n", + "Measurement counts: {'000000000000000011011': 3, '000000000000000011111': 1, '000000000000000100000': 3, '000000000000000100001': 1, '000000000000000101011': 1, '000000000000000111000': 1, '000000000000000111111': 1, '000000000000001000010': 2, '000000000000001000100': 1, '000000000000001000110': 1, '000000000000001001000': 2, '000000000000001001010': 1, '000000000000001010111': 1, '000000000000001100010': 1, '000000000000001100011': 1, '000000000000001100111': 1, '000000000000001101100': 1, '000000000000001101110': 1, '000000000000001101111': 1, '000000000000001110010': 1, '000000000000001111010': 1, '000000100000000000010': 1, '000000100000000000011': 1, '000000100000000000100': 1, '000000100000000001001': 1, '000000100000000010111': 1, '000000100000000011010': 1, '000000100000000011111': 1, '000000100000000100010': 1, '000000100000000100011': 1, '000000100000000100101': 1, '000000100000000101101': 1, '000000100000000101110': 1, '000000100000000110001': 1, 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'111000100000001001111': 1, '111000100000001101111': 1, '111000100000001111010': 1, '111001000000000000000': 1, '111001000000000000101': 1, '111001000000000000110': 1, '111001000000000001101': 1, '111001000000000011100': 1, '111001000000000100100': 1, '111001000000000110110': 1, '111001000000001010000': 1, '111001000000001011101': 1, '111001000000001100011': 1, '111001100000000000001': 2, '111001100000000001011': 1, '111001100000000001110': 1, '111001100000001000001': 1, '111001100000001000010': 1, '111001100000001000100': 1, '111001100000001001110': 1, '111001100000001010000': 1, '111001100000001010111': 1, '111001100000001011100': 1, '111001100000001011111': 1, '111001100000001100101': 1, '111001100000001111001': 1, '111100000000000010000': 1, '111100000000000010011': 1, '111100000000000010111': 1, '111100000000000011110': 1, '111100000000000100100': 1, '111100000000000110011': 1, '111100000000000110101': 1, '111100000000001000110': 1, '111100000000001010101': 1, '111100000000001011000': 1, '111100000000001011101': 1, '111100000000001110011': 1, '111100000000001111110': 1, '111100100000000000000': 1, '111100100000000000100': 3, '111100100000000001100': 1, '111100100000000011010': 1, '111100100000000100001': 2, '111100100000000101100': 1, '111100100000000110110': 1, '111100100000000110111': 1, '111100100000000111101': 1, '111100100000001000000': 1, '111100100000001000101': 1, '111100100000001001100': 1, '111100100000001011100': 1, '111100100000001100110': 1, '111100100000001110001': 1, '111100100000001110011': 1, '111100100000001111011': 1, '111100100000001111111': 1, '111101000000000000001': 1, '111101000000000001101': 1, '111101000000000010101': 1, '111101000000000011101': 1, '111101000000000110101': 1, '111101000000001000100': 2, '111101000000001001100': 1, '111101000000001001101': 1, '111101000000001001110': 1, '111101000000001010010': 1, '111101000000001010111': 1, '111101000000001011101': 1, '111101000000001111100': 1, '111101100000000000101': 1, '111101100000000001100': 1, '111101100000000001101': 1, '111101100000000010001': 1, '111101100000000011001': 1, '111101100000000100101': 1, '111101100000000100111': 1, '111101100000000101111': 1, '111101100000001001111': 1, '111101100000001010000': 1, '111101100000001110000': 1}\n", + "Estimated Betti Number: 7.0000\n", + "Measurement counts: {'000000000000000000101': 1, '000000000000000001010': 1, '000000000000000001100': 1, '000000000000000001110': 1, '000000000000000001111': 1, '000000000000000010001': 1, '000000000000000011100': 1, '000000000000000111101': 1, '000000000000000111110': 1, '000000000000000111111': 1, '000000000000001001100': 1, '000000000000001010000': 1, '000000000000001011110': 1, '000000000000001100001': 1, '000000000000001111000': 3, '000000000000001111101': 1, '000000000000001111110': 1, '000000100000000000000': 1, '000000100000000001100': 1, '000000100000000010100': 1, '000000100000000011001': 1, '000000100000000100000': 1, 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'101101100000000101011': 1, '101101100000000110111': 1, '101101100000000111110': 2, '101101100000001011000': 1, '101101100000001101001': 1, '101101100000001101011': 1, '101101100000001111001': 1, '101101100000001111010': 1, '101101100000001111111': 1, '101110000000000000110': 1, '101110000000000001011': 1, '101110000000000001110': 1, '101110000000000101001': 1, '101110000000000101110': 1, '101110000000000111001': 1, '101110000000000111100': 1, '101110000000001000001': 1, '101110000000001001010': 1, '101110000000001011001': 1, '101110000000001011100': 1, '101110000000001101011': 3, '101110000000001101110': 1, '101110000000001111000': 1, '101110000000001111110': 1, '101110100000000101111': 1, '101110100000001000011': 1, '101110100000001001101': 1, '101110100000001001110': 1, '101110100000001011001': 2, '101110100000001011111': 1, '101110100000001110011': 1, '101110100000001110111': 1, '101110100000001111001': 2, '101110100000001111101': 1, '101110100000001111111': 1, '101111000000000001001': 1, '101111000000000011011': 1, '101111000000000101011': 1, '101111000000000111001': 1, '101111000000000111011': 1, '101111000000001011000': 1, '101111000000001011011': 1, '101111000000001011110': 1, '101111000000001101101': 1, '101111000000001110100': 1, '101111000000001111011': 1, '101111100000000100001': 1, '101111100000000101011': 1, '101111100000001011000': 1, '101111100000001011111': 1, '101111100000001101000': 1, '101111100000001101001': 1, '101111100000001101100': 1, '101111100000001101101': 1, '101111100000001101111': 2, '101111100000001111110': 1, '110001100000001011001': 1, '110110000000001100011': 1, '110110100000001011101': 1, '111001000000001101000': 1, '111001100000000111010': 1, '111010100000001001000': 1, '111011100000001101110': 1, '111111000000000101011': 1}\n", + "Estimated Betti Number: 9.5000\n", + "Measurement counts: {'000000000000000001100': 1, '000000000000000001110': 1, '000000000000000011001': 1, '000000000000000110001': 1, 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'111110000000000101111': 1, '111110000000000111100': 1, '111110000000001001110': 1, '111110000000001001111': 1, '111110000000001010000': 1, '111110000000001011000': 1, '111110000000001011010': 1, '111110000000001101000': 1, '111110000000001110000': 1, '111110000000001110001': 1, '111110000000001111011': 1, '111110000000001111110': 1, '111110000000001111111': 1, '111110100000000001001': 1, '111110100000000110111': 1, '111110100000000111111': 1, '111110100000001101010': 1, '111110100000001101100': 1, '111111000000000000001': 1, '111111000000000001010': 3, '111111000000000011100': 1, '111111000000000100010': 1, '111111000000000100110': 1, '111111000000000101001': 1, '111111000000000111000': 1, '111111000000001000000': 1, '111111000000001000010': 1, '111111000000001011011': 1, '111111000000001111010': 1, '111111000000001111100': 1, '111111100000000100010': 1, '111111100000000101011': 1, '111111100000000101111': 1, '111111100000000110001': 1, '111111100000001001100': 1, '111111100000001001101': 1, '111111100000001001110': 2, '111111100000001010100': 1, '111111100000001010110': 1, '111111100000001011010': 2, '111111100000001100101': 1}\n", + "Estimated Betti Number: 3.1250\n", + "Measurement counts: {'000000100000000011001': 1, '000001000000000000100': 1, '000001100000000010000': 1, '000100000000000011100': 1, '000100000000001010010': 1, '000100100000000001011': 1, '000100100000001001000': 1, '000101000000000100000': 1, '000101000000001001101': 1, '000101000000001100111': 1, '000101100000001011000': 1, '001000100000000001011': 1, '001100000000001001000': 1, '010000000000000001010': 2, '010000000000001010001': 1, '010000100000000001100': 1, '010000100000000011001': 1, '010000100000000101111': 1, '010001000000000001011': 1, '010001000000001001011': 1, '010100000000001000001': 1, '010100100000000011100': 1, '010100100000001101111': 1, '010101000000001110010': 1, '100000000000000000001': 2, '100000000000000000010': 1, '100000000000000000011': 2, 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'111111000000000011000': 1}\n", + "Estimated Betti Number: 8.6250\n", + "Measurement counts: {'000000000000000111101': 1, '000000100000000000001': 1, '000000100000000000100': 1, '000010000000001111101': 1, '000010100000001001010': 1, '000011000000001001000': 1, '000011000000001111101': 1, '000100000000000000001': 1, '000100000000000000110': 1, '000100000000000001000': 2, '000100000000000001001': 1, '000100000000000011000': 1, '000100000000000100010': 1, '000100000000000101010': 1, '000100000000000101110': 2, '000100000000000110110': 1, '000100000000000111010': 1, '000100000000001001011': 1, '000100000000001011000': 1, '000100000000001011010': 1, '000100000000001011101': 1, '000100000000001011110': 1, '000100000000001100111': 1, '000100000000001101001': 1, '000100000000001101100': 1, '000100000000001110011': 1, '000100000000001111111': 1, '000100100000000001000': 1, '000100100000000011000': 1, '000100100000000011010': 1, '000100100000000011100': 1, '000100100000000011101': 1, 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'111101000000001011000': 1, '111101000000001011110': 1, '111101000000001100011': 1, '111101000000001100101': 1, '111101000000001111101': 1, '111101100000000000100': 1, '111101100000000010111': 1, '111101100000000011111': 1, '111101100000000100111': 1, '111101100000000101111': 1, '111101100000000110100': 1, '111101100000000111011': 2, '111101100000000111110': 1, '111101100000001000111': 1, '111101100000001001011': 1, '111101100000001011010': 1, '111110000000000000000': 1, '111110000000000001010': 1, '111110000000000001011': 1, '111110000000000001101': 1, '111110000000000001111': 1, '111110000000000011011': 1, '111110000000001001001': 1, '111110000000001001100': 1, '111110000000001010101': 1, '111110000000001011000': 1, '111110000000001101010': 1, '111110100000000000111': 1, '111110100000000010101': 1, '111110100000000011011': 1, '111110100000000101001': 1, '111110100000000110110': 1, '111110100000001000010': 2, '111110100000001011101': 1, '111110100000001101010': 1, '111110100000001101011': 1, '111110100000001101100': 1, '111110100000001101101': 1, '111110100000001110011': 1, '111110100000001111001': 1, '111111000000000000010': 1, '111111000000000000011': 1, '111111000000000011000': 1, '111111000000000111010': 2, '111111000000001000011': 1, '111111000000001001100': 1, '111111000000001100001': 1, '111111000000001100010': 1, '111111000000001100100': 2, '111111000000001101011': 1, '111111000000001110000': 1, '111111100000000010010': 1, '111111100000000010100': 1, '111111100000000101110': 1, '111111100000000110001': 1, '111111100000000110110': 1, '111111100000001001001': 1, '111111100000001001101': 1, '111111100000001010111': 1, '111111100000001011100': 1, '111111100000001101100': 1, '111111100000001101110': 1, '111111100000001101111': 1}\n", + "Estimated Betti Number: 0.3750\n", + "Measurement counts: {'000000000000000100000': 1, '000000000000001000101': 1, '000000000000001001001': 1, '000000000000001001100': 1, '000000000000001010101': 1, 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'111111100000001000111': 1, '111111100000001010100': 1, '111111100000001101100': 1}\n", + "Estimated Betti Number: 3.5000\n", + "Measurement counts: {'000000000000000000111': 1, '000000000000000001111': 1, '000000000000000010001': 1, '000000000000000010011': 1, '000000000000000010110': 1, '000000000000000010111': 1, '000000000000000011111': 1, '000000000000000110111': 1, '000000000000000111001': 1, '000000000000001000001': 1, '000000000000001000101': 1, '000000000000001000110': 1, '000000000000001000111': 1, '000000000000001010000': 1, '000000000000001010011': 1, '000000000000001010110': 1, '000000000000001011000': 2, '000000000000001011011': 1, '000000000000001011101': 1, '000000000000001111100': 1, '000000000000001111110': 1, '000000100000000000001': 1, '000000100000000000010': 1, '000000100000000000100': 1, '000000100000000001111': 1, '000000100000000010000': 1, '000000100000000010110': 1, '000000100000000010111': 1, '000000100000000011001': 1, '000000100000000011100': 1, 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'011111000000000111100': 1, '011111000000001000110': 1, '011111000000001001001': 1, '011111000000001010100': 1, '011111000000001010111': 1, '011111000000001011101': 1, '011111000000001110010': 1, '011111100000000001011': 1, '011111100000000111001': 1, '011111100000001000000': 1, '011111100000001011001': 1, '101100100000000101110': 1, '101111000000000110100': 1, '110110000000000011000': 1}\n", + "Estimated Betti Number: 9.7500\n", + "Measurement counts: {'000000000000000000111': 1, '000000000000000001000': 2, '000000000000000001101': 1, '000000000000000011001': 1, '000000000000000011110': 1, '000000000000000111011': 1, '000000000000000111101': 1, '000000000000001000010': 1, '000000000000001101000': 1, '000000000000001110011': 1, '000000000000001111001': 1, '000000000000001111101': 1, '000000100000000000001': 1, '000000100000000001010': 1, '000000100000000100000': 1, '000000100000000100011': 1, '000000100000000111000': 1, '000000100000000111011': 1, '000000100000001000000': 1, 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'111100100000001011000': 1, '111100100000001100001': 1, '111100100000001101000': 1, '111100100000001111000': 1, '111101000000000000001': 1, '111101000000000110001': 1, '111101000000000110010': 1, '111101000000000111011': 1, '111101000000001010000': 1, '111101000000001111001': 1, '111101100000000011001': 1, '111101100000001001110': 1}\n", + "Estimated Betti Number: 14.6250\n", + "Measurement counts: {'000000000000000000010': 1, '000000000000000001101': 2, '000000000000000001111': 1, '000000000000000100000': 2, '000000000000000100111': 1, '000000000000000110001': 1, '000000000000001100010': 1, '000000100000000000001': 1, '000000100000000011001': 1, '000000100000000101101': 1, '000001000000000000000': 1, '000001000000000001001': 1, '000001000000000011101': 1, '000001000000001001101': 1, '000001000000001011011': 1, '000001000000001100100': 1, '000001000000001100101': 1, '000001000000001101011': 1, '000001100000000001001': 1, '000001100000000010001': 1, '000001100000000010011': 1, 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'011100000000001000011': 1, '011100000000001000110': 1, '011100000000001010011': 1, '011100000000001011000': 1, '011100000000001011001': 2, '011100000000001011011': 1, '011100000000001100001': 1, '011100000000001100010': 1, '011100000000001101011': 1, '011100000000001110010': 2, '011100000000001111011': 1, '011100100000000000011': 1, '011100100000000000110': 1, '011100100000000000111': 1, '011100100000000001001': 1, '011100100000000001101': 1, '011100100000000010001': 2, '011100100000000011101': 1, '011100100000000100000': 1, '011100100000000110011': 1, '011100100000000111011': 1, '011100100000001000100': 1, '011100100000001001000': 1, '011100100000001001011': 1, '011100100000001010000': 1, '011100100000001010001': 2, '011100100000001010010': 1, '011100100000001010101': 1, '011100100000001010111': 1, '011100100000001011100': 1, '011100100000001100000': 1, '011100100000001101011': 1, '011100100000001111001': 1, '011101000000000000010': 1, '011101000000000000101': 1, '011101000000000000110': 1, '011101000000000001010': 1, '011101000000000001011': 1, '011101000000000001111': 1, '011101000000000010001': 1, '011101000000000010010': 1, '011101000000000010011': 1, '011101000000000010100': 2, '011101000000000011001': 1, '011101000000000011011': 2, '011101000000000101011': 1, '011101000000001000001': 1, '011101000000001010101': 1, '011101000000001011000': 1, '011101000000001011001': 2, '011101000000001101010': 1, '011101000000001101111': 2, '011101000000001110010': 1, '011101000000001110110': 1, '011101000000001110111': 1, '011101000000001111101': 1, '011101100000000000000': 1, '011101100000000000011': 2, '011101100000000000100': 1, '011101100000000001111': 1, '011101100000000010001': 1, '011101100000000011001': 1, '011101100000000011111': 1, '011101100000000100000': 1, '011101100000000101001': 1, '011101100000000110001': 1, '011101100000000110011': 1, '011101100000000110101': 1, '011101100000000111101': 1, '011101100000001000001': 1, '011101100000001000010': 1, '011101100000001000011': 1, '011101100000001001011': 1, '011101100000001010001': 1, '011101100000001010011': 1, '011101100000001011000': 1, '011101100000001011010': 1, '011101100000001011011': 1, '011101100000001100011': 1, '011101100000001101011': 1, '011101100000001101101': 1, '011101100000001110000': 1, '011101100000001111001': 1, '011110000000000001100': 1, '011110000000000010101': 1, '011110000000000010111': 1, '011110000000000100011': 1, '011110000000000101011': 1, '011110000000000101101': 1, '011110000000000110001': 1, '011110000000000111101': 1, '011110000000000111111': 2, '011110000000001000011': 1, '011110000000001011101': 1, '011110000000001011110': 1, '011110000000001100000': 1, '011110000000001100010': 1, '011110000000001101001': 1, '011110000000001111001': 1, '011110100000000000011': 2, '011110100000000001011': 2, '011110100000000010000': 1, '011110100000000010011': 2, '011110100000000011010': 1, '011110100000000011011': 2, '011110100000000110001': 1, '011110100000000110111': 1, '011110100000000111001': 1, '011110100000000111101': 1, '011110100000001000001': 1, '011110100000001001010': 2, '011110100000001001011': 1, '011110100000001100011': 1, '011110100000001110011': 1, '011111000000000000001': 1, '011111000000000011001': 1, '011111000000000011011': 1, '011111000000000101001': 1, '011111000000000111000': 1, '011111000000000111011': 1, '011111000000000111110': 1, '011111000000001000001': 1, '011111000000001000100': 1, '011111000000001001001': 1, '011111000000001001011': 1, '011111000000001001100': 1, '011111000000001001101': 1, '011111000000001010000': 2, '011111000000001010010': 1, '011111000000001100101': 1, '011111000000001101000': 2, '011111000000001110001': 2, '011111000000001110101': 1, '011111100000000000000': 1, '011111100000000000011': 1, '011111100000000000111': 1, '011111100000000001011': 1, '011111100000000001100': 1, '011111100000000010001': 1, '011111100000000011001': 1, '011111100000000011011': 2, '011111100000000011101': 1, '011111100000000100000': 1, '011111100000000110011': 1, '011111100000000110111': 1, '011111100000001000001': 1, '011111100000001000011': 1, '011111100000001000100': 2, '011111100000001000111': 1, '011111100000001001000': 1, '011111100000001010110': 1, '011111100000001011000': 1, '011111100000001011001': 1, '011111100000001100001': 1, '011111100000001100011': 1, '011111100000001101101': 1, '011111100000001110111': 1, '011111100000001111111': 1, '100011100000000001011': 1, '101110100000001101000': 1, '101111000000001110001': 1, '110000000000001011100': 1, '110001100000000010001': 1, '110001100000000110001': 1, '110001100000001000101': 1, '110011000000001100001': 1, '110111100000000011111': 1, '111001000000000011010': 1, '111010100000000001100': 1, '111011000000000011100': 1, '111011000000001011011': 1, '111100100000000000011': 1, '111100100000000100000': 1, '111101000000000010000': 1, '111101000000001011001': 1, '111110100000000000101': 1, '111110100000001000011': 1, '111111100000000100000': 1, '111111100000001001011': 1}\n", + "Estimated Betti Number: 3.7500\n", + "Measurement counts: {'000000100000001110010': 1, '000010000000000010111': 1, '000010000000000011100': 1, '000010100000001010011': 1, '000011000000000001011': 1, '000011100000000010010': 1, '000110100000000001011': 1, '000110100000001100111': 1, '000111000000001100110': 1, '000111100000000011101': 1, '001011100000000000010': 1, '001011100000000100111': 1, '001110000000000001010': 1, '001110100000000011110': 1, '001110100000000100110': 1, '001110100000001000010': 1, '001111000000001000000': 1, '001111000000001001110': 1, '001111100000000011011': 1, '010000000000000000000': 1, '010000100000000010000': 1, '010000100000001000001': 1, '010000100000001000101': 1, '010000100000001010001': 1, '010001000000000000001': 1, '010001000000000010001': 1, '010001000000000111100': 1, '010001000000001010110': 1, '010001100000000000110': 1, '010001100000000010011': 1, '010001100000000011111': 1, '010001100000001111101': 1, '010010000000000000000': 2, '010010000000000000001': 1, '010010000000000000100': 2, '010010000000000000101': 2, '010010000000000000110': 3, '010010000000000000111': 2, '010010000000000001010': 2, '010010000000000001011': 1, '010010000000000010000': 1, '010010000000000010010': 1, '010010000000000010011': 1, '010010000000000010110': 2, '010010000000000010111': 2, '010010000000000011011': 3, '010010000000000011101': 1, '010010000000000011110': 1, '010010000000000011111': 2, '010010000000000100001': 1, '010010000000000100010': 1, '010010000000000100110': 1, '010010000000000100111': 1, '010010000000000101001': 1, '010010000000000101111': 1, '010010000000000110000': 1, '010010000000000110010': 1, '010010000000000110011': 2, '010010000000000110100': 1, '010010000000000110101': 1, '010010000000000110111': 1, '010010000000000111001': 1, '010010000000001000010': 1, '010010000000001000011': 2, 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'011110000000000000001': 2, '011110000000000000011': 1, '011110000000000000100': 1, '011110000000000000101': 1, '011110000000000001100': 1, '011110000000000001111': 1, '011110000000000010000': 1, '011110000000000010110': 3, '011110000000000010111': 1, '011110000000000011010': 1, '011110000000000011100': 2, '011110000000000011110': 1, '011110000000000011111': 1, '011110000000000100000': 1, '011110000000000100010': 1, '011110000000000101111': 1, '011110000000000110011': 1, '011110000000000111101': 1, '011110000000000111110': 1, '011110000000000111111': 2, '011110000000001000011': 1, '011110000000001000100': 1, '011110000000001000101': 1, '011110000000001000111': 2, '011110000000001001010': 1, '011110000000001001011': 1, '011110000000001001110': 5, '011110000000001001111': 1, '011110000000001010000': 1, '011110000000001010001': 1, '011110000000001010010': 1, '011110000000001010101': 1, '011110000000001010110': 3, '011110000000001010111': 1, '011110000000001011011': 2, '011110000000001011110': 2, '011110000000001100101': 1, '011110000000001100110': 1, '011110000000001101000': 1, '011110000000001101111': 1, '011110000000001110001': 1, '011110000000001110011': 1, '011110000000001111001': 1, '011110000000001111010': 1, '011110000000001111011': 1, '011110000000001111101': 1, '011110100000000000001': 1, '011110100000000000101': 1, '011110100000000000110': 2, '011110100000000000111': 2, '011110100000000001010': 1, '011110100000000001011': 1, '011110100000000010000': 1, '011110100000000010010': 2, '011110100000000010011': 1, '011110100000000010111': 2, '011110100000000011011': 1, '011110100000000011110': 1, '011110100000000011111': 1, '011110100000000100110': 1, '011110100000000100111': 2, '011110100000000101010': 2, '011110100000000101101': 1, '011110100000000101111': 1, '011110100000000110010': 1, '011110100000000110100': 1, '011110100000000110110': 1, '011110100000000110111': 1, '011110100000000111111': 2, '011110100000001000000': 1, 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'011111000000000011010': 2, '011111000000000011100': 1, '011111000000000110000': 1, '011111000000000110011': 1, '011111000000000110100': 1, '011111000000000110101': 2, '011111000000000110110': 1, '011111000000000110111': 1, '011111000000000111000': 1, '011111000000000111010': 1, '011111000000001000000': 1, '011111000000001000011': 1, '011111000000001000100': 1, '011111000000001000101': 2, '011111000000001000111': 2, '011111000000001001000': 3, '011111000000001001010': 1, '011111000000001001110': 1, '011111000000001001111': 1, '011111000000001010001': 1, '011111000000001010011': 1, '011111000000001010100': 2, '011111000000001010101': 2, '011111000000001010111': 2, '011111000000001011011': 1, '011111000000001011110': 1, '011111000000001100000': 1, '011111000000001101001': 1, '011111000000001101100': 2, '011111000000001110101': 1, '011111000000001110111': 1, '011111100000000000010': 1, '011111100000000000111': 3, '011111100000000001001': 1, '011111100000000001010': 1, '011111100000000001011': 2, '011111100000000001101': 1, '011111100000000010101': 1, '011111100000000011000': 1, '011111100000000100110': 1, '011111100000000110010': 2, '011111100000000110100': 1, '011111100000000110110': 2, '011111100000000111010': 1, '011111100000000111110': 1, '011111100000000111111': 1, '011111100000001000000': 1, '011111100000001000100': 2, '011111100000001000101': 1, '011111100000001000110': 1, '011111100000001001001': 2, '011111100000001001111': 1, '011111100000001010010': 2, '011111100000001010011': 1, '011111100000001010110': 1, '011111100000001011101': 2, '011111100000001011110': 1, '011111100000001011111': 1, '011111100000001101001': 1, '011111100000001110111': 1, '011111100000001111000': 1, '011111100000001111001': 1, '011111100000001111101': 1, '011111100000001111111': 1, '110000000000000011010': 1, '110010000000001000110': 1, '110011100000000010100': 1, '110011100000000010110': 1, '110011100000001010110': 1, '110110000000000001001': 1, '110110100000001011010': 1, '110111000000001101001': 1, '110111100000000001011': 1, '110111100000000100010': 1, '110111100000001000000': 1, '110111100000001100010': 1, '111000100000000100010': 1, '111010000000000011101': 1, '111010000000001011000': 1, '111010100000000010111': 1, '111010100000001011110': 1, '111011000000001000100': 1, '111011000000001000110': 1, '111011000000001010001': 1, '111011100000000010011': 1, '111011100000000101000': 1, '111110000000000011110': 1, '111110000000001000101': 1}\n", + "Estimated Betti Number: 0.1250\n", + "Measurement counts: {'000000000000000001110': 1, '000000000000000010001': 1, '000000000000000010010': 1, '000000000000000011000': 1, '000000000000000110010': 1, '000000000000000111010': 3, '000000000000000111100': 1, '000000000000001000000': 1, '000000000000001000001': 1, '000000000000001001110': 1, '000000000000001010000': 1, '000000000000001011001': 1, '000000000000001011010': 1, '000000000000001100011': 1, '000000000000001101010': 1, 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'011111100000000011110': 1, '011111100000000110011': 1, '011111100000000111010': 1, '011111100000000111100': 1, '011111100000001000100': 1, '011111100000001001100': 1, '011111100000001010101': 1, '011111100000001100010': 1, '011111100000001100101': 1, '011111100000001111001': 1, '011111100000001111110': 2, '100010100000001001111': 1, '100111100000000011100': 1, '100111100000001111111': 1, '101011000000001111010': 1, '101100100000000111011': 1, '101111000000000010100': 1, '101111100000001100111': 1, '111101000000001001000': 1}\n", + "Estimated Betti Number: 7.6250\n", + "Measurement counts: {'000000000000000000000': 2, '000000000000000000001': 1, '000000000000000000011': 1, '000000000000000001100': 1, '000000000000000010000': 1, '000000000000000011000': 1, '000000000000000011101': 2, '000000000000000110011': 1, '000000000000000111000': 1, '000000000000001001100': 1, '000000000000001001101': 1, '000000000000001001111': 1, '000000000000001010000': 1, '000000000000001010100': 1, 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'111100100000000111111': 1, '111100100000001000001': 1, '111100100000001000111': 1, '111100100000001001000': 1, '111100100000001010001': 2, '111100100000001100001': 1, '111100100000001110011': 1, '111100100000001111001': 1, '111101000000000000001': 1, '111101000000000000101': 1, '111101000000000011110': 1, '111101000000000100011': 1, '111101000000000100111': 1, '111101000000000101111': 1, '111101000000000110101': 1, '111101000000001001110': 1, '111101000000001001111': 1, '111101000000001010000': 1, '111101000000001010101': 1, '111101000000001011101': 1, '111101000000001100001': 1, '111101000000001101111': 1, '111101000000001110001': 1, '111101000000001110100': 1, '111101100000000000100': 1, '111101100000000010010': 1, '111101100000000010110': 1, '111101100000000011101': 1, '111101100000000011111': 1, '111101100000000100001': 1, '111101100000000101001': 1, '111101100000000110001': 1, '111101100000001000111': 1, '111101100000001001000': 1, '111101100000001001111': 1, '111101100000001010111': 1, '111101100000001011111': 1, '111101100000001101001': 1, '111101100000001101010': 1, '111101100000001110011': 2, '111101100000001110111': 1, '111101100000001111111': 1}\n", + "Estimated Betti Number: 9.6250\n", + "Measurement counts: {'000001000000000111001': 1, '000011100000001100011': 1, '000100000000000000000': 1, '000100000000000001101': 1, '000100000000000011100': 2, '000100000000000011101': 1, '000100000000000100011': 1, '000100000000000110010': 2, '000100000000000110100': 1, '000100000000000111100': 1, '000100000000001001101': 1, '000100000000001001111': 1, '000100000000001011001': 1, '000100000000001011101': 1, '000100000000001101000': 1, '000100000000001111110': 1, '000100100000000000110': 1, '000100100000000001100': 1, '000100100000000010001': 1, '000100100000000011111': 1, '000100100000000101110': 1, '000100100000001001000': 1, '000100100000001001001': 1, '000100100000001010110': 1, '000100100000001011110': 1, '000100100000001011111': 1, 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'111101100000000101111': 1, '111101100000000110011': 1, '111101100000000110101': 1, '111101100000001001000': 1, '111101100000001001101': 1, '111101100000001001110': 1, '111101100000001010011': 1, '111101100000001010100': 1, '111101100000001011001': 1, '111101100000001011011': 1, '111101100000001100001': 1, '111101100000001101010': 1, '111101100000001111011': 1, '111110000000000001001': 1, '111110000000000001111': 1, '111110000000000010011': 1, '111110000000000100100': 1, '111110000000000101000': 1, '111110000000000101001': 1, '111110000000000101110': 1, '111110000000000110110': 2, '111110000000000111000': 1, '111110000000001000010': 1, '111110000000001010110': 1, '111110000000001011011': 1, '111110000000001110111': 1, '111110000000001111000': 1, '111110000000001111001': 2, '111110100000000000001': 1, '111110100000000000011': 1, '111110100000000001111': 1, '111110100000000011001': 1, '111110100000000011100': 1, '111110100000000011110': 1, '111110100000000100111': 1, '111110100000000101100': 1, '111110100000000101101': 1, '111110100000000111110': 1, '111110100000001000010': 1, '111110100000001001010': 1, '111110100000001011000': 2, '111110100000001110100': 1, '111110100000001110111': 1, '111110100000001111011': 1, '111111000000000000001': 1, '111111000000000000101': 1, '111111000000000001011': 1, '111111000000000001101': 1, '111111000000000010101': 1, '111111000000000010111': 1, '111111000000000100010': 1, '111111000000000101110': 1, '111111000000000110010': 1, '111111000000000110011': 1, '111111000000001001011': 1, '111111000000001011101': 1, '111111000000001100010': 1, '111111000000001100111': 1, '111111000000001101111': 1, '111111000000001111010': 1, '111111000000001111100': 1, '111111100000000000011': 1, '111111100000000010001': 1, '111111100000000010101': 1, '111111100000000011110': 1, '111111100000000110011': 1, '111111100000001011010': 1, '111111100000001100101': 1, '111111100000001110110': 1}\n", + "Estimated Betti Number: 0.1250\n", + "Measurement counts: {'000000000000000000000': 1, '000000000000000000100': 2, '000000000000000000101': 1, '000000000000000010111': 1, '000000000000000011111': 1, '000000000000000100000': 1, '000000000000000101000': 1, '000000000000000101111': 1, '000000000000000110011': 1, '000000000000000110101': 1, '000000000000000110110': 1, '000000000000001000110': 1, '000000000000001001001': 1, '000000000000001010111': 1, '000000000000001011000': 1, '000000000000001011010': 1, '000000000000001011111': 1, '000000000000001101000': 1, '000000000000001101010': 1, '000000000000001110111': 1, '000000000000001111010': 1, '000000100000000000100': 1, '000000100000000000101': 1, '000000100000000000110': 1, '000000100000000001101': 1, '000000100000000010000': 2, '000000100000000100000': 2, '000000100000000101010': 1, '000000100000000101110': 1, '000000100000000110011': 1, '000000100000000110111': 1, '000000100000000111000': 1, '000000100000000111111': 1, '000000100000001001101': 1, '000000100000001010010': 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'101110000000001101000': 1, '101110000000001101001': 1, '101110000000001101011': 1, '101110000000001111000': 1, '101110100000000000000': 1, '101110100000000001000': 1, '101110100000000001011': 1, '101110100000000010001': 1, '101110100000000010011': 1, '101110100000000010100': 1, '101110100000000010110': 1, '101110100000000011010': 1, '101110100000000100100': 1, '101110100000000110011': 1, '101110100000001001001': 1, '101110100000001001011': 1, '101110100000001100000': 1, '101110100000001100111': 1, '101110100000001101001': 1, '101110100000001101011': 1, '101111000000000001000': 1, '101111000000000001010': 1, '101111000000000001011': 1, '101111000000000100010': 1, '101111000000000100100': 1, '101111000000000100110': 1, '101111000000000101011': 1, '101111000000000111000': 1, '101111000000001000001': 1, '101111000000001000101': 1, '101111000000001000110': 1, '101111000000001001000': 1, '101111000000001001011': 1, '101111000000001001101': 1, '101111000000001001111': 1, '101111000000001010001': 1, '101111000000001100101': 1, '101111000000001101011': 1, '101111000000001101111': 1, '101111000000001110110': 1, '101111000000001111001': 1, '101111100000000101111': 1, '101111100000001001101': 1, '101111100000001001111': 2, '101111100000001011010': 1, '101111100000001100001': 1, '101111100000001110001': 1, '101111100000001111010': 1, '101111100000001111101': 1, '110000100000001000010': 1, '110101100000000111000': 1, '111000000000001101010': 1}\n", + "Estimated Betti Number: 8.8750\n", + "Measurement counts: {'000000000000000100000': 1, '000000000000001000111': 1, '000000000000001001001': 1, '000000000000001010110': 1, '000000100000000000110': 1, '000000100000000000111': 1, '000000100000000001101': 1, '000000100000001001100': 1, '000000100000001011011': 1, '000000100000001011100': 1, '000000100000001110001': 1, '000001000000000000111': 1, '000001000000000001111': 1, '000001000000000010010': 1, '000001000000000010011': 1, '000001000000000100110': 1, 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'111111100000001101101': 1}\n", + "Estimated Betti Number: 3.1250\n", + "Measurement counts: {'000010000000000011010': 1, '000011000000000011001': 1, '000011000000000101101': 1, '001000000000001001110': 1, '001000100000000010100': 1, '001001000000001001010': 1, '001001100000001101010': 1, '001001100000001101011': 1, '001001100000001110101': 1, '001010000000000101100': 1, '001010000000000110101': 1, '001011000000000011010': 1, '001011100000000000000': 1, '010000000000001000101': 1, '010001000000001010110': 1, '010001100000001010000': 1, '010011000000000110101': 1, '011001000000001010011': 1, '011001000000001101000': 1, '100000000000000000011': 1, '100000000000000001010': 1, '100000000000000001011': 1, '100000000000000001111': 1, '100000000000000010000': 2, '100000000000000010010': 2, '100000000000000011101': 1, '100000000000000100110': 1, '100000000000000101000': 1, '100000000000000101100': 1, '100000000000000110011': 1, '100000000000000110100': 2, '100000000000000110101': 1, 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'011100100000001011100': 1, '011100100000001011101': 1, '011100100000001101010': 1, '011100100000001111001': 1, '011100100000001111100': 1, '011101000000000000110': 1, '011101000000000001100': 1, '011101000000000010100': 1, '011101000000000011000': 1, '011101000000000101110': 1, '011101000000000110000': 1, '011101000000000110010': 1, '011101000000000110111': 1, '011101000000001000001': 1, '011101000000001000011': 1, '011101000000001001010': 1, '011101000000001011010': 1, '011101000000001011101': 1, '011101000000001100011': 1, '011101000000001110010': 1, '011101000000001110101': 1, '011101000000001110111': 1, '011101100000000000001': 1, '011101100000000010111': 1, '011101100000000011100': 1, '011101100000000101000': 1, '011101100000000101101': 1, '011101100000001001011': 1, '011101100000001001110': 1, '011101100000001010101': 1, '011101100000001100101': 1, '011101100000001100111': 1, '011101100000001101111': 1, '011101100000001110101': 1, '011110000000000001011': 1, '011110000000000010100': 1, '011110000000000101101': 2, '011110000000000101111': 1, '011110000000000110001': 1, '011110000000000110010': 1, '011110000000000111010': 1, '011110000000001000100': 1, '011110000000001001101': 1, '011110000000001010011': 1, '011110000000001010100': 1, '011110000000001011011': 1, '011110000000001011101': 3, '011110000000001110000': 1, '011110000000001111111': 1, '011110100000000000011': 1, '011110100000000010011': 1, '011110100000000011001': 1, '011110100000000011111': 1, '011110100000000100101': 1, '011110100000000110000': 1, '011110100000000111111': 1, '011110100000001001110': 1, '011110100000001001111': 1, '011110100000001010010': 1, '011110100000001011001': 1, '011110100000001101010': 1, '011110100000001101100': 1, '011110100000001110000': 1, '011110100000001110010': 1, '011110100000001111110': 1, '011111000000000001000': 1, '011111000000000001100': 1, '011111000000000011011': 1, '011111000000000011101': 1, '011111000000000100100': 1, '011111000000000100101': 1, '011111000000000101000': 1, '011111000000000110100': 1, '011111000000000111001': 1, '011111000000001011000': 1, '011111000000001011110': 1, '011111000000001100110': 1, '011111000000001110001': 1, '011111000000001111011': 2, '011111100000000000011': 1, '011111100000000000100': 1, '011111100000000000111': 1, '011111100000000001111': 1, '011111100000000010111': 1, '011111100000000011000': 1, '011111100000000011010': 1, '011111100000000011100': 1, '011111100000000100000': 1, '011111100000000101101': 1, '011111100000000111001': 1, '011111100000000111011': 1, '011111100000000111111': 1, '011111100000001001011': 1, '011111100000001110010': 1, '100010000000001111110': 1, '100011000000000100100': 1, '100011000000001001110': 1, '100100000000000101010': 1, '100100000000000110111': 1, '100100000000001000000': 1, '100101000000000110101': 1, '100101000000001100011': 1, '100111000000001000000': 1, '101010100000000100011': 1, '101100000000001000101': 1, '101100100000001101010': 1, '101101000000001111101': 1, '101111100000000101111': 1, '110010000000001011110': 1, '110100000000000000001': 1, '110100000000000011000': 1, '110111000000001101000': 1, '110111000000001110100': 1, '111000100000001101011': 1, '111001000000000100011': 1, '111001000000001100011': 1, '111010100000000011010': 1, '111110000000000001111': 1, '111110000000001000100': 1}\n", + "Estimated Betti Number: 6.7500\n", + "Measurement counts: {'000000000000000001001': 1, '000000000000000100110': 1, '000000000000000101000': 1, '000000000000000101011': 1, '000000000000000111001': 1, '000000000000001010000': 1, '000000000000001011011': 1, '000000000000001101110': 1, '000001000000000010011': 1, '000001000000000101101': 1, '000001000000000101111': 1, '000001000000000110111': 1, '000001000000001001010': 1, '000001000000001010000': 1, '000001000000001100101': 1, '000001000000001101001': 1, '000001000000001110100': 1, '000001000000001111011': 1, '000010000000000001011': 1, 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'111010000000000101101': 1, '111010000000000101111': 1, '111010000000000111111': 1, '111010000000001000011': 1, '111010000000001100010': 1, '111010000000001110100': 2, '111010000000001110101': 1, '111010000000001111110': 1, '111011000000000010001': 1, '111011000000000011100': 2, '111011000000000011111': 1, '111011000000000101001': 1, '111011000000000101101': 1, '111011000000000111000': 1, '111011000000000111110': 1, '111011000000001001000': 1, '111011000000001001111': 2, '111011000000001010010': 1, '111011000000001011010': 1, '111011000000001100000': 1, '111011000000001100001': 1, '111011000000001100100': 1, '111011000000001100110': 1, '111011000000001111111': 1, '111100000000000001100': 1, '111100000000000011001': 1, '111100000000000011101': 1, '111100000000000100111': 1, '111100000000000101010': 1, '111100000000001000010': 1, '111100000000001000101': 1, '111100000000001001111': 1, '111100000000001010010': 1, '111100000000001100100': 2, '111100000000001100110': 1, '111100100000000001011': 1, '111101000000000000000': 1, '111101000000000000100': 1, '111101000000000000111': 1, '111101000000000001100': 1, '111101000000000001110': 1, '111101000000000011000': 1, '111101000000000100001': 1, '111101000000000100101': 1, '111101000000001000101': 1, '111101000000001001000': 1, '111101000000001001100': 1, '111101000000001010100': 1, '111101000000001011001': 1, '111101000000001100001': 1, '111101000000001101101': 1, '111101000000001111100': 1, '111101100000000111101': 1, '111110000000000001101': 1, '111110000000000010001': 1, '111110000000000100010': 1, '111110000000000101001': 1, '111110000000000101110': 1, '111110000000000111110': 1, '111110000000001001001': 1, '111110000000001001010': 1, '111110000000001001011': 1, '111110000000001011011': 1, '111110000000001100010': 1, '111110000000001101000': 1, '111110000000001101100': 1, '111110000000001101111': 1, '111110000000001110110': 1, '111110000000001111100': 2, '111111000000000000011': 1, '111111000000000001101': 1, '111111000000000100111': 1, '111111000000000111001': 1, '111111000000000111111': 1, '111111000000001001000': 1, '111111000000001001001': 1, '111111000000001001100': 2, '111111000000001001101': 2, '111111000000001011111': 1, '111111000000001100011': 1, '111111000000001100110': 2, '111111000000001100111': 2, '111111000000001101000': 1, '111111000000001101001': 1, '111111000000001101100': 1}\n", + "Estimated Betti Number: 2.2500\n", + "Measurement counts: {'000000000000000110011': 1, '000000000000000110100': 1, '000000000000000110111': 1, '000000000000001000100': 1, '000000000000001001011': 1, '000000000000001001100': 1, '000000000000001101111': 1, '000000000000001110100': 1, '000000000000001111001': 1, '000000100000000001110': 1, '000000100000000011011': 1, '000000100000000101000': 1, '000000100000000111100': 1, '000000100000001111101': 1, '000001000000000100010': 2, '000001000000000101010': 1, '000001000000000110110': 1, '000001000000000110111': 1, 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'111110000000000110001': 1, '111110000000000110101': 1, '111110000000000111110': 1, '111110000000001000101': 1, '111110000000001001100': 1, '111110000000001111100': 1, '111110100000000000100': 1, '111110100000000001010': 1, '111110100000000001110': 1, '111110100000000011010': 1, '111110100000000100100': 1, '111110100000000101100': 1, '111110100000000110110': 1, '111110100000001010010': 1, '111110100000001011000': 1, '111110100000001100101': 1, '111111000000000000100': 1, '111111000000000111011': 2, '111111000000001001001': 1, '111111000000001001111': 1, '111111000000001100010': 1, '111111100000000000111': 1, '111111100000000011010': 1, '111111100000000100001': 1, '111111100000000100100': 1, '111111100000000111001': 1, '111111100000000111100': 1, '111111100000001010001': 1, '111111100000001101101': 1, '111111100000001111000': 1, '111111100000001111001': 1}\n", + "Estimated Betti Number: 4.2500\n", + "Measurement counts: {'000000000000000000011': 1, '000000000000000011101': 1, 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'111101100000001101010': 1, '111110000000000110100': 1, '111110100000001001101': 1}\n", + "Estimated Betti Number: 8.1250\n", + "Measurement counts: {'000001100000000010010': 1, '000010000000000000000': 1, '000010000000000001011': 1, '000010000000000010000': 1, '000010000000000011000': 1, '000010000000000100000': 1, '000010000000000100001': 1, '000010000000000100100': 1, '000010000000000101001': 2, '000010000000000101100': 2, '000010000000000110111': 1, '000010000000001000010': 2, '000010000000001000100': 1, '000010000000001000111': 1, '000010000000001001000': 1, '000010000000001001111': 1, '000010000000001010001': 1, '000010000000001011011': 1, '000010000000001100110': 1, '000010000000001101000': 1, '000010000000001110010': 1, '000010000000001111110': 1, '000010100000000001010': 1, '000010100000000010000': 1, '000010100000000011000': 1, '000010100000000011001': 1, '000010100000000100101': 1, '000010100000000100111': 1, '000010100000000101101': 1, '000010100000000101110': 1, 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'110111100000001111110': 1, '111000000000000100001': 1, '111010000000000000111': 1, '111010000000000001110': 2, '111010000000000101110': 1, '111010000000000110110': 1, '111010000000001000011': 1, '111010000000001000100': 1, '111010000000001001010': 1, '111010000000001001111': 1, '111010000000001011101': 1, '111010000000001011111': 1, '111010000000001100010': 2, '111010000000001100100': 1, '111010100000000000000': 1, '111010100000000010111': 1, '111010100000000011110': 1, '111010100000000011111': 1, '111010100000000100001': 1, '111010100000000110010': 1, '111010100000001000101': 1, '111010100000001001001': 1, '111010100000001001011': 1, '111010100000001010000': 1, '111010100000001011011': 1, '111010100000001100110': 1, '111010100000001100111': 1, '111010100000001101000': 1, '111011000000000000100': 1, '111011000000000001010': 1, '111011000000000001011': 1, '111011000000000001110': 1, '111011000000000010000': 1, '111011000000000010011': 1, '111011000000000011001': 1, '111011000000000110111': 1, '111011000000000111100': 1, '111011000000001001000': 1, '111011000000001001100': 1, '111011000000001010001': 1, '111011000000001010011': 1, '111011000000001100010': 1, '111011000000001100101': 1, '111011000000001110001': 1, '111011100000000010011': 1, '111011100000000010110': 1, '111011100000000011010': 1, '111011100000000100000': 1, '111011100000000100010': 1, '111011100000000101110': 1, '111011100000000101111': 1, '111011100000001000001': 1, '111011100000001001010': 1, '111011100000001001100': 1, '111011100000001010000': 1, '111011100000001010111': 1, '111011100000001011111': 1, '111011100000001100000': 2, '111011100000001111011': 1, '111100100000001010000': 1, '111100100000001100101': 1, '111110000000000001100': 1, '111110000000000010001': 1, '111110000000000100111': 1, '111110000000000101000': 1, '111110000000000101110': 1, '111110000000001000101': 1, '111110000000001001000': 1, '111110000000001010110': 1, '111110000000001011011': 1, '111110000000001100000': 1, '111110000000001100100': 1, '111110000000001100110': 1, '111110000000001101000': 1, '111110000000001101011': 1, '111110000000001101110': 1, '111110000000001111010': 1, '111110100000000000111': 1, '111110100000000001100': 1, '111110100000000010001': 1, '111110100000000011111': 1, '111110100000001001010': 1, '111110100000001001110': 1, '111110100000001011101': 1, '111110100000001011110': 1, '111110100000001100100': 1, '111110100000001100101': 1, '111110100000001100110': 1, '111110100000001101111': 1, '111111000000000000010': 1, '111111000000000000111': 1, '111111000000000010010': 1, '111111000000000010111': 1, '111111000000000011011': 1, '111111000000000100111': 1, '111111000000001000000': 1, '111111000000001000001': 1, '111111000000001000110': 1, '111111000000001100011': 1, '111111000000001101100': 1, '111111000000001111001': 1, '111111000000001111111': 1, '111111100000000000000': 1, '111111100000000001001': 2, '111111100000000001111': 1, '111111100000000100100': 1, '111111100000000110001': 1, '111111100000000110111': 1, '111111100000000111001': 1, '111111100000001000001': 1, '111111100000001000010': 1, '111111100000001001010': 1, '111111100000001001111': 1, '111111100000001011001': 1, '111111100000001011011': 1, '111111100000001011111': 1, '111111100000001100011': 1, '111111100000001111111': 2}\n", + "Estimated Betti Number: 0.1250\n", + "Measurement counts: {'000000100000000001110': 1, '000000100000001011001': 1, '000001000000000011101': 1, '000001000000000111000': 1, '000001000000000111100': 1, '000001000000001000110': 1, '000001000000001011111': 1, '000001000000001100011': 1, '000001100000000001111': 1, '000001100000000011110': 1, '000001100000001010001': 1, '000001100000001100001': 1, '000001100000001101101': 1, '000001100000001110101': 1, '000010000000000001101': 1, '000010000000001001111': 1, '000011000000000001000': 1, '000011000000001001110': 1, '000011000000001101010': 1, '000011000000001110000': 1, 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'110111000000001010010': 1, '110111000000001010101': 1, '110111000000001011001': 1, '110111000000001011011': 1, '110111000000001011101': 1, '110111000000001100011': 1, '110111000000001100100': 2, '110111000000001101110': 1, '110111000000001110000': 1, '110111000000001111011': 1, '110111000000001111100': 1, '110111100000000000000': 1, '110111100000000000011': 3, '110111100000000001011': 1, '110111100000000001100': 1, '110111100000000001101': 1, '110111100000000010011': 1, '110111100000000010110': 1, '110111100000000100010': 1, '110111100000000100100': 1, '110111100000000100111': 2, '110111100000000101001': 3, '110111100000000101110': 1, '110111100000000110111': 1, '110111100000000111011': 1, '110111100000000111101': 1, '110111100000001000010': 2, '110111100000001000100': 1, '110111100000001000111': 1, '110111100000001001000': 1, '110111100000001001001': 3, '110111100000001001100': 1, '110111100000001010001': 1, '110111100000001011100': 1, '110111100000001100101': 3, '110111100000001101000': 1, '110111100000001101001': 1, '110111100000001101010': 1, '110111100000001101100': 1, '110111100000001111101': 1, '111001000000001010110': 1, '111001000000001101010': 1, '111001000000001110001': 1, '111001100000000010110': 1, '111001100000000100101': 1, '111001100000001011110': 1, '111001100000001101100': 1, '111010000000001000011': 1, '111010000000001010111': 1, '111011000000001100110': 1, '111011000000001100111': 1, '111011000000001101001': 1, '111011000000001101010': 1, '111011100000000000010': 1, '111011100000000000101': 1, '111011100000000101100': 1, '111011100000001000011': 1, '111011100000001101100': 1, '111101000000001000010': 1, '111101100000000011001': 1, '111101100000001000011': 1, '111101100000001100011': 1, '111111000000000010000': 1, '111111000000001000100': 1, '111111000000001001101': 1, '111111000000001001110': 1, '111111100000000011011': 1, '111111100000001001000': 1}\n", + "Estimated Betti Number: 1.7500\n", + "Measurement counts: {'000000000000000001101': 1, '000000000000000010000': 1, '000000000000000010100': 1, '000000000000000011010': 1, '000000000000000011011': 1, '000000000000000011101': 1, '000000000000000110110': 1, '000000000000001110101': 1, '000000100000000000100': 1, '000000100000000011100': 1, '000000100000000011101': 1, '000000100000000101110': 1, '000000100000000110111': 1, '000000100000000111110': 1, '000000100000001010011': 1, '000000100000001011001': 1, '000000100000001100000': 1, '000000100000001101111': 1, '000000100000001110100': 1, '000000100000001111000': 1, '000001000000000000100': 1, '000001000000000001101': 1, '000001000000000010100': 1, '000001000000000101000': 1, '000001000000000101111': 1, '000001000000000111000': 1, '000001000000001001001': 1, '000001000000001010011': 1, '000001000000001010100': 1, '000001000000001111010': 1, '000001100000000000011': 1, '000001100000000001000': 1, '000001100000000010001': 1, '000001100000001010010': 1, '000001100000001010101': 1, 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'111111100000001001100': 1, '111111100000001010100': 1, '111111100000001011000': 2, '111111100000001011010': 1, '111111100000001011011': 1, '111111100000001110111': 1}\n", + "Estimated Betti Number: 4.8750\n", + "Measurement counts: {'000000000000000001101': 1, '000000000000000010010': 1, '000000000000000011010': 1, '000000000000000011110': 1, '000000000000000100001': 1, '000000000000001100000': 1, '000000000000001100111': 1, '000000000000001101100': 1, '000000000000001110111': 1, '000000000000001111000': 1, '000000100000000000111': 1, '000000100000000010110': 1, '000000100000000100100': 1, '000000100000000100110': 1, '000000100000000110111': 1, '000000100000000111101': 1, '000000100000001011100': 1, '000000100000001100000': 1, '000000100000001100110': 1, '000000100000001101110': 1, '000000100000001110110': 1, '000000100000001111110': 1, '000001000000000000101': 1, '000001000000000001110': 1, '000001000000000101110': 1, '000001000000000111001': 1, '000001000000000111110': 1, 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'111111100000000000110': 1, '111111100000000111101': 1, '111111100000001000101': 1, '111111100000001100100': 1, '111111100000001101100': 1}\n", + "Estimated Betti Number: 4.8750\n", + "Measurement counts: {'000000000000000000111': 1, '000000000000000101011': 1, '000000000000000110001': 1, '000000000000000110010': 1, '000000000000000111001': 1, '000000000000000111111': 1, '000000000000001010111': 1, '000000000000001011001': 1, '000000000000001011101': 1, '000000000000001101110': 1, '000000000000001111100': 1, '000000000000001111111': 1, '000000100000000001000': 1, '000000100000000001010': 1, '000000100000000001101': 1, '000000100000000100011': 1, '000000100000000111011': 1, '000000100000001000001': 1, '000000100000001001110': 1, '000000100000001010010': 1, '000000100000001011100': 1, '000001000000000010010': 1, '000001000000000101001': 1, '000001000000000110110': 1, '000001000000001000000': 1, '000001000000001001111': 1, '000001000000001110000': 1, '000001000000001110001': 1, 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'110001100000001011001': 1, '110001100000001100000': 1, '110001100000001100001': 1, '110001100000001111000': 1, '110001100000001111001': 1, '110010000000000010011': 1, '110010000000000011011': 1, '110010000000000101001': 2, '110010000000001000010': 1, '110010000000001000111': 1, '110010000000001001001': 1, '110010000000001010011': 1, '110010000000001010101': 1, '110010000000001011100': 1, '110010000000001111011': 1, '110010100000000001101': 1, '110010100000000100101': 1, '110010100000000110101': 1, '110010100000001000010': 1, '110010100000001100001': 1, '110010100000001100100': 1, '110010100000001101001': 1, '110010100000001110011': 1, '110011000000000000101': 1, '110011000000000001001': 1, '110011000000000111001': 1, '110011000000000111101': 1, '110011000000001001100': 1, '110011000000001110111': 1, '110011000000001111000': 1, '110011100000000000000': 1, '110011100000000001001': 1, '110011100000000011000': 1, '110011100000000011001': 1, '110011100000000011101': 1, '110011100000000111010': 1, '110011100000001001110': 1, '110011100000001011111': 1, '110011100000001101000': 1, '110011100000001101011': 1, '110011100000001101101': 1, '110011100000001110111': 1, '110100000000000010110': 1, '110100000000000011000': 1, '110100000000000011010': 2, '110100000000000111000': 1, '110100000000001001010': 1, '110100000000001001101': 1, '110100000000001011000': 1, '110100000000001011001': 1, '110100000000001101111': 1, '110100000000001110001': 3, '110100000000001111101': 1, '110100100000000000001': 1, '110100100000000000010': 1, '110100100000000001100': 1, '110100100000000010011': 1, '110100100000000011110': 1, '110100100000000100111': 1, '110100100000000110000': 1, '110100100000001000110': 1, '110100100000001001000': 1, '110100100000001001011': 1, '110100100000001111011': 1, '110101000000000000111': 1, '110101000000000010101': 1, '110101000000000010110': 1, '110101000000000011101': 1, '110101000000000011110': 1, '110101000000000100010': 1, 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'110111100000001011110': 1, '110111100000001101011': 1, '111000000000000000111': 1, '111000000000000010000': 1, '111000000000001000000': 1, '111000000000001100011': 1, '111000000000001111000': 1, '111000100000000000001': 1, '111000100000000000100': 1, '111000100000001010010': 1, '111000100000001100110': 1, '111001000000000001000': 1, '111001000000000010001': 1, '111001000000000010010': 1, '111001000000000010110': 1, '111001000000000011001': 1, '111001000000000011100': 1, '111001000000001111001': 1, '111001100000000001000': 1, '111001100000000010100': 1, '111001100000000100100': 1, '111001100000001000000': 1, '111001100000001100111': 1, '111001100000001101001': 1, '111001100000001111110': 1, '111001100000001111111': 1, '111010000000000010000': 1, '111010000000001000100': 1, '111010100000000000011': 1, '111010100000000001110': 1, '111010100000000001111': 1, '111010100000000011001': 1, '111010100000000101110': 1, '111010100000001010110': 1, '111011000000000000000': 1, '111011000000000010011': 2, '111011000000000010100': 2, '111011000000000011011': 1, '111011000000001011000': 1, '111011000000001111000': 2, '111011100000000011001': 1, '111011100000000110110': 1, '111011100000001011100': 1, '111011100000001110010': 1, '111100000000000011111': 1, '111100000000000100101': 1, '111100000000000101010': 1, '111100000000000101100': 1, '111100000000000111001': 1, '111100000000001000000': 1, '111100000000001011100': 1, '111100000000001011101': 1, '111100000000001100100': 1, '111100000000001101001': 1, '111100000000001111110': 1, '111100100000000000100': 1, '111100100000000111000': 1, '111100100000001010010': 1, '111100100000001101110': 1, '111101000000000100111': 1, '111101000000000111010': 1, '111101000000001011010': 1, '111101000000001101110': 1, '111101100000000001001': 1, '111101100000000001100': 2, '111101100000000011001': 1, '111101100000001010111': 1, '111101100000001100111': 1, '111110000000000000001': 1, '111110000000000100010': 1, '111110000000001100001': 1, '111110100000000000111': 1, '111110100000000010000': 1, '111110100000001011001': 1, '111111000000000110010': 1, '111111000000000111100': 1, '111111000000001100001': 1, '111111000000001100011': 1, '111111100000000000101': 1, '111111100000000010000': 1, '111111100000000011011': 1, '111111100000001010110': 1, '111111100000001101011': 1}\n", + "Estimated Betti Number: 4.6250\n", + "Measurement counts: {'000000000000000011000': 1, '000000100000000000100': 1, '000000100000000100101': 1, '000000100000000101111': 1, '000000100000001000100': 1, '000000100000001100010': 1, '000000100000001101110': 1, '000000100000001111001': 1, '000001000000001101000': 1, '000001100000000001000': 1, '000001100000000010010': 1, '000001100000000011101': 1, '000001100000000100010': 1, '000001100000000101001': 1, '000001100000000111011': 1, '000001100000001000011': 1, '000001100000001000101': 1, '000001100000001010011': 1, '000001100000001100101': 1, '000001100000001101010': 1, 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'111111100000001101011': 1}\n", + "Estimated Betti Number: 2.5000\n", + "Measurement counts: {'000000000000000000000': 1, '000000000000000000011': 1, '000000000000000000100': 1, '000000000000000010010': 1, '000000000000000010110': 1, '000000000000000100000': 1, '000000000000000100101': 1, '000000000000000101110': 1, '000000000000001001100': 1, '000000000000001001110': 1, '000000000000001101011': 1, '000000000000001110000': 1, '000000000000001110010': 2, '000000000000001110101': 1, '000000100000000000001': 1, '000000100000000000100': 1, '000000100000000000111': 1, '000000100000000001100': 1, '000000100000000001101': 1, '000000100000000100010': 1, '000000100000000100111': 1, '000000100000000101001': 1, '000000100000000111101': 1, '000000100000001000000': 1, '000000100000001000110': 3, '000000100000001010000': 2, '000000100000001100100': 1, '000001000000000000010': 1, '000001000000000000111': 1, '000001000000000001000': 1, '000001000000000001111': 1, '000001000000000010011': 1, 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'101111000000000110110': 1, '101111000000000111000': 1, '101111000000000111001': 1, '101111000000000111010': 1, '101111000000000111011': 1, '101111000000001000000': 1, '101111000000001000001': 1, '101111000000001000100': 1, '101111000000001001101': 1, '101111000000001010011': 1, '101111000000001011000': 1, '101111000000001011100': 1, '101111000000001111110': 1, '101111100000000000001': 2, '101111100000000000010': 1, '101111100000000000011': 1, '101111100000000001011': 1, '101111100000000001110': 2, '101111100000000010110': 2, '101111100000000011000': 1, '101111100000000011001': 1, '101111100000000011011': 1, '101111100000000011100': 1, '101111100000000011101': 1, '101111100000000011110': 1, '101111100000000011111': 1, '101111100000000100011': 1, '101111100000000100111': 1, '101111100000000110000': 1, '101111100000000110001': 1, '101111100000000110010': 1, '101111100000000110011': 2, '101111100000000110100': 1, '101111100000000110110': 1, '101111100000000111010': 1, '101111100000000111101': 1, '101111100000001010010': 1, '101111100000001010101': 1, '101111100000001010110': 1, '101111100000001011010': 1, '101111100000001011110': 3, '101111100000001100001': 1, '101111100000001111001': 1, '101111100000001111010': 1, '101111100000001111011': 2, '101111100000001111110': 1, '110010100000000110011': 1, '110111000000001111111': 1, '110111100000001100001': 1, '111010100000000000010': 1, '111011000000000000100': 1, '111011000000000111111': 1, '111100000000000001010': 1}\n", + "Estimated Betti Number: 0.1250\n", + "Measurement counts: {'000000000000000001000': 1, '000000000000000110010': 1, '000000000000001010111': 1, '000000000000001101001': 1, '000001000000001100011': 1, '000010000000001000001': 1, '000010000000001011010': 1, '000011000000000110011': 1, '000011000000001000010': 1, '000011000000001110110': 1, '000100000000000000100': 1, '000100000000001010100': 1, '000101000000000011011': 1, '000101000000001011001': 1, '000101000000001100101': 1, 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'111001000000001011001': 1, '111010100000000011010': 1, '111010100000001001100': 1, '111110100000000100100': 1, '111111100000000000100': 1, '111111100000000000110': 1}\n", + "Estimated Betti Number: 8.6250\n", + "Measurement counts: {'000000000000000010001': 1, '000000000000000010110': 1, '000000000000000011001': 1, '000000000000000101000': 1, '000000000000000101010': 1, '000000000000000101101': 1, '000000000000001000000': 1, '000000000000001000110': 1, '000000000000001001000': 1, '000000000000001001001': 1, '000000000000001001011': 1, '000000000000001010000': 2, '000000000000001010001': 1, '000000000000001010100': 1, '000000000000001010101': 1, '000000000000001011010': 1, '000000000000001011110': 1, '000000000000001100011': 1, '000000000000001101100': 1, '000000100000000000110': 1, '000000100000000011001': 2, '000000100000000011110': 1, '000000100000000101010': 1, '000000100000000110001': 1, '000000100000000111000': 1, '000000100000001001011': 1, '000000100000001011000': 1, 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'111100100000001101000': 1, '111100100000001101111': 1, '111100100000001111101': 1, '111110000000000110010': 1, '111110000000001001010': 1, '111110000000001101010': 1, '111110000000001111110': 2, '111110100000000001100': 1, '111110100000000010001': 1, '111110100000000010101': 1, '111110100000000011001': 1, '111110100000000100000': 1, '111110100000000100011': 2, '111110100000000101110': 1, '111110100000000110011': 1, '111110100000000111010': 1, '111110100000001110000': 1, '111110100000001110110': 1, '111110100000001111010': 1}\n", + "Estimated Betti Number: 4.1250\n", + "Measurement counts: {'000000000000000000000': 1, '000000000000000000011': 1, '000000000000000000111': 1, '000000000000000001101': 1, '000000000000000001111': 1, '000000000000000010011': 1, '000000000000000011010': 1, '000000000000000100010': 1, '000000000000000100111': 1, '000000000000000101010': 1, '000000000000000101011': 1, '000000000000000111010': 1, '000000000000000111100': 2, '000000000000001001010': 1, 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'111101100000001100111': 1, '111101100000001101000': 1, '111101100000001101010': 1, '111101100000001101011': 1, '111101100000001110001': 1, '111110000000000000000': 1, '111110000000000000101': 1, '111110000000000001000': 1, '111110000000000001010': 1, '111110000000000010101': 1, '111110000000000011010': 1, '111110000000000011101': 1, '111110000000000101010': 1, '111110000000000101110': 1, '111110000000001000011': 1, '111110000000001001101': 1, '111110000000001010010': 1, '111110000000001101000': 1, '111110000000001110010': 1, '111110000000001111111': 1, '111110100000001010101': 1, '111110100000001011110': 1, '111110100000001110010': 1, '111110100000001111011': 2, '111110100000001111100': 1, '111111000000000000001': 1, '111111000000000001111': 1, '111111000000000010100': 1, '111111000000000100110': 1, '111111000000000101011': 1, '111111000000000110011': 1, '111111000000001001111': 1, '111111000000001010111': 1, '111111000000001011011': 1, '111111000000001100011': 2, 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'101110000000000000010': 1, '101110000000000000110': 1, '101110000000000001011': 1, '101110000000000011100': 1, '101110000000000101011': 1, '101110000000000101111': 1, '101110000000001000000': 1, '101110000000001001000': 1, '101110000000001001100': 1, '101110000000001001110': 1, '101110000000001100001': 1, '101110000000001100100': 1, '101110000000001101000': 1, '101110000000001111001': 1, '101110000000001111111': 1, '101110100000000000100': 1, '101110100000000001011': 1, '101110100000000101000': 1, '101110100000000101001': 1, '101110100000000110101': 1, '101110100000001000010': 1, '101110100000001001101': 1, '101110100000001100110': 1, '101110100000001101001': 1, '101110100000001101111': 1, '101110100000001110111': 1, '101111000000000000001': 1, '101111000000000000110': 1, '101111000000000001011': 1, '101111000000000100010': 1, '101111000000000100100': 2, '101111000000000101000': 1, '101111000000000101010': 2, '101111000000000110001': 1, '101111000000001000111': 1, '101111000000001011011': 1, '101111000000001011100': 1, '101111000000001011111': 1, '101111000000001101111': 1, '101111000000001111001': 1, '101111000000001111111': 1, '101111100000000001000': 1, '101111100000000011010': 1, '101111100000000100011': 1, '101111100000000100110': 1, '101111100000000101000': 1, '101111100000000101011': 1, '101111100000000101111': 1, '101111100000000111010': 1, '101111100000001100000': 1, '101111100000001101101': 1, '101111100000001101110': 2, '110001000000000001000': 1, '110001100000000010101': 1, '110001100000001011000': 1, '110010000000000000010': 1, '110010000000000001010': 1, '110011000000000100111': 1, '110011100000001111100': 1, '110100100000001101110': 1, '110110100000001011110': 1, '110111000000001011010': 1, '111000100000000101110': 1, '111000100000001111101': 1, '111011000000000110001': 1, '111011100000000001110': 1, '111100100000001100001': 1, '111101000000000001111': 1, '111101000000001100001': 1}\n", + "Estimated Betti Number: 7.5000\n", + "Measurement counts: {'000000000000000000111': 1, '000000000000000001000': 1, '000000000000000010010': 1, '000000000000000011010': 1, '000000000000000101100': 1, '000000000000000101101': 1, '000000000000000101110': 1, '000000000000000110000': 1, '000000000000000110010': 1, '000000000000000110011': 1, '000000000000000110100': 1, '000000000000000111011': 1, '000000000000000111101': 1, '000000000000000111110': 1, '000000000000001000001': 1, '000000000000001000100': 1, '000000000000001001001': 1, '000000000000001001100': 1, '000000000000001010011': 1, '000000000000001011010': 1, '000000000000001011101': 1, '000000000000001100000': 1, '000000000000001100010': 1, '000000000000001100100': 1, '000000000000001100101': 2, '000000000000001100111': 2, '000000000000001101000': 2, '000000000000001101011': 1, '000000000000001110101': 1, '000000000000001111010': 1, '000000000000001111011': 1, '000000000000001111110': 1, '000000100000000010000': 1, '000000100000000010011': 1, '000000100000000100011': 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'111101000000000101001': 1, '111101000000000111010': 1, '111101000000001000010': 2, '111101000000001000011': 1, '111101000000001010001': 2, '111101000000001011100': 1, '111101000000001011101': 1, '111101000000001100011': 1, '111101100000001000001': 1, '111101100000001001111': 1, '111101100000001010000': 1, '111101100000001010010': 1, '111101100000001010111': 1, '111101100000001011000': 1, '111101100000001100001': 1, '111101100000001110010': 1, '111110000000001001100': 1, '111110100000000101110': 1, '111110100000001001101': 1, '111111100000000101010': 1}\n", + "Estimated Betti Number: 10.7500\n", + "Measurement counts: {'000000000000000011011': 1, '000000000000000110011': 1, '000000000000000110110': 1, '000000000000000110111': 1, '000000000000000111101': 1, '000000000000001000010': 1, '000000000000001000011': 1, '000000000000001010000': 1, '000000100000000001100': 1, '000000100000000011001': 1, '000000100000000101001': 1, '000000100000000110000': 1, '000000100000000111111': 1, 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'111111100000001011111': 1}\n", + "Estimated Betti Number: 4.2500\n", + "Measurement counts: {'000000000000000001100': 1, '000000000000000001101': 1, '000000000000000001110': 1, '000000000000000011100': 1, '000000000000000100001': 1, '000000000000000100011': 1, '000000000000000110111': 1, '000000000000000111011': 1, '000000000000000111101': 1, '000000000000000111111': 1, '000000000000001000001': 1, '000000000000001000110': 1, '000000000000001001000': 1, '000000000000001001001': 1, '000000000000001001110': 1, '000000000000001010000': 2, '000000000000001010100': 2, '000000000000001010111': 1, '000000000000001011001': 2, '000000000000001011111': 1, '000000000000001100000': 1, '000000000000001100010': 1, '000000000000001100101': 1, '000000000000001101000': 1, '000000000000001101010': 1, '000000000000001101011': 1, '000000000000001101100': 1, '000000000000001110011': 1, '000000000000001110101': 1, '000000000000001110111': 1, '000000000000001111110': 1, '000000100000000011101': 1, 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'111000000000001011101': 1, '111000100000000001001': 1, '111000100000000001110': 1, '111000100000000100010': 1, '111000100000000111001': 1, '111000100000001010110': 1, '111000100000001110000': 1, '111001000000000010111': 1, '111001000000000011010': 1, '111001000000001000101': 1, '111001000000001001101': 1, '111001000000001010101': 1, '111001000000001110000': 1, '111001000000001111001': 1, '111001100000000000000': 1, '111001100000000000011': 1, '111001100000000011010': 1, '111001100000000100000': 1, '111001100000000101001': 1, '111001100000000110111': 1, '111001100000001000010': 1, '111001100000001001100': 1, '111001100000001001110': 1, '111001100000001011110': 2, '111010000000000000100': 1, '111010000000000100110': 1, '111010000000000101000': 1, '111010000000000110111': 1, '111010000000000111011': 1, '111010000000000111101': 1, '111010000000001000110': 1, '111010000000001110011': 1, '111010000000001111011': 1, '111010100000000100000': 1, '111010100000000110000': 1, '111010100000000111101': 1, '111010100000001001111': 1, '111010100000001010010': 1, '111010100000001100010': 1, '111011000000000100010': 1, '111011000000000110001': 1, '111011000000000110111': 1, '111011000000001011011': 1, '111011000000001100110': 1, '111011000000001101001': 1, '111011100000000010101': 1, '111011100000000100000': 1, '111011100000000101001': 1, '111011100000001010000': 1, '111011100000001110011': 1, '111100000000001011110': 1, '111100000000001100101': 1, '111100000000001101010': 1, '111100100000000011111': 1, '111100100000000100001': 1, '111100100000000101010': 1, '111100100000000110000': 1, '111100100000000110001': 1, '111100100000000111011': 1, '111100100000001000100': 1, '111100100000001000110': 1, '111100100000001010110': 1, '111100100000001010111': 1, '111101000000000010100': 1, '111101000000000100000': 1, '111101000000000100011': 1, '111101000000000111111': 1, '111101000000001000111': 1, '111101000000001110000': 1, '111101000000001110001': 1, '111101100000000010000': 1, '111101100000000010100': 1, '111101100000000100010': 1, '111101100000001000000': 1, '111101100000001000111': 1, '111101100000001011101': 1, '111101100000001111011': 1, '111110000000000010100': 1, '111110000000001000000': 1, '111110000000001011110': 1, '111110000000001100111': 1, '111110100000000001010': 1, '111110100000000001101': 1, '111110100000000010001': 1, '111110100000000110001': 1, '111110100000001000100': 1, '111110100000001100000': 1, '111111000000000010100': 1, '111111000000000100011': 1, '111111000000001110010': 1, '111111000000001110101': 2, '111111100000000000100': 1, '111111100000001001111': 1, '111111100000001101010': 1}\n", + "Estimated Betti Number: 5.6250\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import gudhi\n", + "from scipy.linalg import expm\n", + "import numpy as np\n", + "\n", + "# Import Qiskit\n", + "from qiskit import QuantumCircuit, transpile\n", + "from qiskit_aer import AerSimulator\n", + "from qiskit.visualization import plot_histogram, plot_state_city\n", + "import qiskit.quantum_info as qi\n", + "time_series = pd.read_csv(r\"sp500_full.csv\",header=None)\n", + "time_series=time_series[1]\n", + "time_series = np.log(time_series).to_numpy().squeeze()\n", + "# time_series = np.log(pd.read_csv(r\"/content/2025-Moodys/sp500.csv\", header=None).to_numpy().squeeze())\n", + "\n", + "\n", + "betty_value_per_epsilon =[]\n", + "for epsilon in np.arange(1,5,1): # Ensure the upper bound is inclusive15\n", + " point_cloud = generate_point_cloud(time_series, N=4, d=15, w=15)\n", + " print()\n", + " grouped_simplices_per_filtration = generate_simplex_groups(point_cloud, epsilon)\n", + "\n", + " betty_values= generate_betti_numbers(grouped_simplices_per_filtration)\n", + " print(betty_values)\n", + " betty_value_per_epsilon.append(betty_values)\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "KEea_z3oxdPA" + }, + "outputs": [], + "source": [ + "U_range = list(map(list, zip(*betty_value_per_epsilon)))\n", + "print(len(U_range),len(U_range[0]))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "H0vlN_ZhGVnX" + }, + "outputs": [], + "source": [ + "U_range" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "L9h-pxdpzdIN" + }, + "outputs": [], + "source": [ + "components = U_range\n", + "# Calculate distances between components\n", + "components = np.array(components)\n", + "components = np.rint(components).astype(int)\n", + "\n", + "distances = [np.linalg.norm(components[i] - components[i + 1]) for i in range(len(components) - 1)]\n", + "\n", + "# Print distances\n", + "len(distances)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "cK1EcxE50ekW" + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# Example data: Replace with your actual list of 130 elements\n", + "data = distances\n", + "\n", + "# Min-max scaling\n", + "min_val = min(data)\n", + "max_val = max(data)\n", + "scaled_data = [(x - min_val) / (max_val - min_val) for x in data] if max_val != min_val else [0] * len(data)\n", + "\n", + "# Plot the scaled line chart\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot(range(1, len(scaled_data) + 1), scaled_data, marker='o', linestyle='-', color='b', label='Scaled Data Trend')\n", + "\n", + "# Labels and Title\n", + "plt.xlabel(\"Index\")\n", + "plt.ylabel(\"Scaled Value (0 to 1)\")\n", + "plt.title(\"Scaled Line Chart for 130 Elements\")\n", + "plt.grid(True)\n", + "plt.legend()\n", + "\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "2Tr_ylf6mAgG" + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}