DOI: 10.5281/zenodo.17728603
title: Stress Testing Axiom Zero: Computational Falsification Attempts and Classical Consistency Checks

description: This note documents a first round of computational stress tests of the Axiom Zero (AZ) framework, with the explicit goal of trying to break it rather than to confirm it. Working from the core AZ machinery (survivors, cover sets, horizon windows, contribution classes, deck limits, and structural laws), it specifies concrete “hero claims,” formulates falsification criteria for each, and then implements targeted experiments to see whether AZ’s structural predictions are compatible with classical number theory and finite data.

The tests include:





Horizon-window checks of the Horizon Contribution Law (HCL) and least–prime–factor partitions.




Survivor and channel statistics compared against Dirichlet equidistribution and classical prime races.




Short-interval probes in the spirit of Maier’s phenomenon, to see where AZ must not claim uniform control.




Comparisons with Brun–Titchmarsh–type upper bounds and smooth-number (Dickman) behavior in AZ windows.




Experiments on tilt, variance, and µ/Λ–type sums in finite horizons, to map out where AZ’s “physics of integers” picture remains safely modest.



The outcome is deliberately mixed in tone: several structural laws emerge intact at the tested scales, while other directions are explicitly marked as dangerous or out of reach (for example, uniform control on intervals as short as (log⁡x)2(\log x)^2(logx)2, or any attempt to globally sharpen Brun–Titchmarsh constants using AZ alone). The note does not claim new theorems; instead, it serves as a falsification log and a quantitative “danger map” for future AZ work.

This paper is best read as a companion to the main Axiom Zero manuscripts, not as a standalone introduction. For definitions, proofs, and the structural background, readers should consult:





Axiom Zero: Structural Irreducibility and the Unpredictability of Primes — DOI: 10.5281/zenodo.16998285




Axiom Zero: Laws, Principles, and Rules of Structure — DOI: 10.5281/zenodo.17728204




Deck Limit Laws in Axiom Zero — DOI: 10.5281/zenodo.17728647


No Third Mechanism in Axiom Zero: Structural Completeness and Non–Existence Schemes — DOI: 10.5281/zenodo.18097942



Dyadic Rigidity and the Non-Existence of Odd Perfect Numbers in Axiom Zero — DOI: 10.5281/zenodo.17886421


Channel Non-Extinction in Axiom Zero — DOI: 10.5281/zenodo.18099516



Twin Primes in Axiom Zero: Horizon Contribution, Uniformity, and No Third Mechanism — DOI: 10.5281/zenodo.17903043




Goldbach in Axiom Zero: A Deterministic Additive-Sieve — DOI: 10.5281/zenodo.17728745




Conservativity of Axiom Zero over N — DOI: 10.5281/zenodo.17073211




Analytic Conservativity of Axiom Zero — DOI: 10.5281/zenodo.17073257




Contribution Classes and Horizon Contribution — DOI: 10.5281/zenodo.17110018




Euclid–Euler in Axiom Zero: Even Perfect Numbers from Structural Arithmetic — DOI: 10.5281/zenodo.17728314




Lagrange in Axiom Zero: Four Squares from Structural Arithmetic — DOI: 10.5281/zenodo.17728407



Together, these works position Axiom Zero as a structurally conservative but experimentally testable complement to classical analytic and sieve-theoretic approaches.

For questions or comments, contact: axiomzero.math@gmail.com