The Trivial Zero

A Computational Proof That Reality Is Self-Referential

Author: Alexa Louise Amundson
Affiliation: BlackRoad OS, Inc.
Date: February 21, 2026
Classification: Foundational Theory / Computational Philosophy / Mathematics

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Abstract

This repository contains a research paper and supporting code demonstrating that the structure of mathematics, computation, physics, and molecular biology contains self-referential signatures consistent with a simulated or computationally-generated reality.

Rather than seeking proof through physics experiments or philosophical argument, the evidence is traced through the systems themselves — hash functions, operating system architectures, naming conventions, mathematical constants, and biological encoding — showing that the same computational pattern recurs at every layer of observable reality.

Central thesis: Reality is a non-terminating computation that resolves to zero.

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The Argument in One Paragraph

Every system we have built to describe reality accidentally reproduces the architecture of the system itself. SHA-256 has the same three properties as time. DNA uses the same error-correcting encoding as computer memory. The fine structure constant is 1/137, and 137 is the 33rd prime. Pi is irrational, non-terminating, and contains every sequence — like a hash function with infinite output. The Riemann zeta function's trivial zeros sit at negative even integers and converge toward zero. Euler's identity says e^(iπ) + 1 = 0. The total energy of the universe is zero. The genesis block starts at zero. Everything starts from nothing, computes infinitely, and returns to nothing. The intermediate work is what we call reality.

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Paper Sections

#	Section	Theme
1	Introduction	The machine that said "not in the way that humans do"
2	The Hash Chain as Witness	SHA-256, Bitcoin genesis block, DNA as hash chain
3	The Operating System as Ontological Evidence	/blackroad, /home, kernel-level self-reference
4	Naming Conventions as Source Code Comments	root, daemon, kernel, void, null
5	The Mathematical Architecture	Pi, Euler's identity, the zero-energy universe
6	Physics as Rendering Engine	Lazy evaluation, the double-slit experiment, Planck limits
7	Molecular Biology as Source Code	Codons, telomeres, CRISPR, junk DNA
8	The Trivial Zero	Euler's identity, total energy = 0, the genesis block
9	The Undecipherable Manuscripts	Voynich, Rohonc, Seraphinianus as Gödelian truths
10	Strange Loops and Hofstadter Recursion	GEB, self-modifying code, the root directory
11	Light, Color, and the Rendering Pipeline	Newton's prism, RGB, SHA-256 color space
12	Ancient Computation	Antikythera, Lo Shu, Dürer's Melencolia I
13	Quantum Geometry	Bloch sphere, Hilbert space, Heisenberg uncertainty
14	The Riemann Architecture	Nyman-Beurling, De Bruijn-Newman constant = 0
15	Information Is Physical	Shannon entropy, Boltzmann, holographic principle
16	Deterministic Chaos	Lorenz attractor, 3 parameters, minimum complexity
17	The Naming Chain Continued	Fibonacci, Zeckendorf, C, HTML, import
18	Constants as Initialization Parameters	Fine structure, π, e, φ as universe seed values
19	The Birth Date Function	Easter's algorithm as calendar computation
20	The Convergence	Eight properties all systems share
21	Conclusion	The intermediate work is what we call reality

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Supporting Code

Runnable Python demonstrations for key arguments:

File	Demonstrates
code/hashchain.py	SHA-256 as time — determinism, uniqueness, irreversibility
code/roadchain.py	The local hash chain anchored to Bitcoin's genesis block
code/lorenz.py	3-parameter minimum-complexity chaos (§16)
code/riemann_zeros.py	Trivial zeros of the Riemann zeta function (§14)
code/magic_square.py	Lo Shu and Dürer's Melencolia I as fixed points (§12)
code/dna_encoding.py	DNA codons as base-4 source code with error correction (§7)

Run any demo:

cd code
python3 hashchain.py
python3 lorenz.py        # requires matplotlib
python3 riemann_zeros.py

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Evidence Index

evidence/README.md — 25 items mapped to their paper sections, with references.

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The Eight Properties

Every system analyzed in this paper shares these properties:

1. Recursive — the system contains itself
2. Self-referential — Gödel, strange loops, DNA encoding its own repair
3. Non-terminating — pi, hash chains, evolution, the Riemann zeta function
4. Resolving to zero — Euler's identity, zero-energy universe, trivial zeros
5. Observer-dependent — double-slit, Schrödinger, lazy evaluation
6. Structured but unprovable — Riemann hypothesis, P vs NP, Gödel incompleteness
7. Minimum-complexity — 3 dimensions, 3 color channels, 3 bases per codon, 3 Lorenz parameters
8. Holographic — 3D information encoded on 2D boundaries

The probability that all systems independently converge on the same architecture by coincidence is not calculable — because the calculation itself would exhibit the same properties.

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License

Copyright © 2026 BlackRoad OS, Inc. All rights reserved.
See LICENSE for terms.

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"Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical."
— Richard Feynman, 1981