1. Project Overview

Project Leviathan investigates the topological origins of the Early Maturity Problem. We propose that the 'impossible' efficiency of high-redshift structures is not a breakdown of physics, but the geometric signature of a Retro-Selective Causal Graph.

This framework challenges the standard forward-chaining stochastic models of ΛCDM by modeling the universe as a directed tree graph where the Present acts as a fixed boundary condition, forcing the past to optimize structurally.

The conputational pipeline performs a rigorous Null-Test Audit across three cosmological epochs to falsify this hypothesis:

1. The High-Z Era: Testing the "Structural Age" of JWST galaxies vs. Coordinate Time.
2. The Cosmic Noon: Testing for Mega-Structures exceeding the Causal Horizon.
3. The CMB Era: Testing the formation rate of the Eridanus Supervoid (Cold Spot).

2. Research Aims (The "Monsters")

We audit anomalies that represent "Causality Breakers" in the standard model.

Audit	Target Anomaly	Metric	The "Impossible" Factor
A. Chronometry	JWST Galaxies ($z > 10$)	Maturity Ratio ($R_m$)	Galaxies appearing older than the Universe's coordinate age.
B. Connectivity	Hercules-Corona Wall	Graph Diameter	Connected structures larger than the causality horizon ($> 1.2$ Gly).
C. Vacuum	The Cold Spot	Void Depth	Supervoids clearing faster than Dark Energy growth allows.

3. Key Findings: The Leviathan Scaling Law

Our audit revealed that the "precocious maturity" of the universe is not limited to specific epochs but follows a continuous global scaling law. We defined a "Rushing Factor" ($R$)—the degree of structural anomaly relative to ΛCDM—and found it scales geometrically with redshift:

$$R(z) \propto (1+z)^{1.26}$$

The Topological Link

This exponent ($1.26$) was originally derived empirically from the data but has now been identified as a topological constant of the universe's causal graph.

• The Prediction: A retro-selective causal tree generates a "Teleological Bias" ($\mathcal{A}$) that scales linearly with system depth ($t$): $$\mathcal{A} \propto t \cdot \ln(k)$$
• The Discovery: By identifying system depth with cosmic expansion (t = ln(1+z)), the observed exponent $1.26$ corresponds to the Logarithmic Branching Factor of the cosmic tree: $$\ln k \approx 1.26 \implies k \approx 3.5$$

This suggests the universe effectively "branches" into ~3.5 causal possibilities at each step, but retro-causal optimization preserves only the single most efficient path, creating the illusion of "impossible" maturity in the early universe.

---

4. Repository Structure

/scripts (Execution Entry Points)

These scripts run specific scientific audits.

Phase I: The Chronometry Audit (JWST)

• audit_early_mass.py: Ingests JWST/JADES catalogs to plot Stellar Mass vs. Available Time. Fits the $\alpha$ exponent.
• audit_maturity.py: Calculates the "Maturity Ratio" for high-z candidates.

Phase II: The Mega-Structure Audit

• audit_connectivity.py: Runs Friends-of-Friends (FoF) clustering on Quasar catalogs to find super-horizon structures.
• run_null_walls.py: Generates random point clouds to test the statistical likelihood of 10-Gly walls.

Phase III: The Void Audit

• audit_cold_spot.py: Cross-correlates Planck SMICA maps with galaxy density (WISE) to test void formation rates.

/src/leviathan/engines (Physics Logic)

Core mathematical modules implementing the specific tests.

• chronometry.py: Implements the $\tau(t)$ integration and Press-Schechter mass limits.
• topology.py: Graph theory algorithms (MST, FoF) for structure detection.
• voids.py: Geodesic distance calculators for void/spot alignment.

/src/leviathan (Core)

• ingestion.py: Standardized loading for Planck, JWST, and SDSS catalogs.
• nulling.py: Generates isotropic Gaussian Random Fields ($C_l$ preserved) for control tests.
• config.py: Central repository of Cosmological Parameters ($H_0$, $\Omega_m$, $\alpha$).

/paper (Theory and Findings)

• proposal.pdf: Original Project Proposal.

  • The initial hypothesis and methodology outline for Project Leviathan.

• theory.pdf: Retro-Causal Optimization in Expanding Graph Topologies.

  • The formal mathematical proof demonstrating that any retro-selective network inevitably generates "precocious maturity" and "teleological bias" artifacts that scale linearly with system depth.

• convergence_law.pdf: The Convergence Law of Cosmic Structure.

  • The primary research paper detailing the data audit, the discovery of the $z^{1.26}$ scaling law, and the empirical evidence for retro-causal optimization.

---

5. Usage

To reproduce the Phase I "Early Bird" audit:

# 1. Clone the repository
git clone [https://github.com/ajhewitt/leviathan](https://github.com/ajhewitt/leviathan)
cd leviathan

# 2. Run the Chronometry Audit (requires astropy)
python scripts/audit_early_mass.py

6. Acknowledgments

Data provided by the Planck Collaboration (2018 Release), JWST (MAST Archive), and SDSS/BOSS. Analysis performed using astropy, healpy, and scipy.

7. License

MIT