What question did this study set out to answer?

The central aim is to establish a local finite theorem for modulus 81 associated with the 3x+1 map.

June 3, 20260 citationsOpen Access

The Local Modulus 81 Theorem

Key Points

The central aim is to establish a local finite theorem for modulus 81 associated with the 3x+1 map.
Developed a reverse-transport model focused on finite parameters at modulus 81.
Conducted computational checks using exact integer and rational arithmetic to verify finite objects.
Provided a reproducibility package including manuscripts, source files, and verification reports.
The theorem proves local finite results but does not address global convergence (no global results given).
Findings include detailed computational verifications of matrix/vector data and residual identities.
Included examples such as a pairing-law counterexample, showcasing specific aspects of the reverse-transport model.

Abstract

This record contains the manuscript and reproducibility package for The Local Modulus-81 Theorem. The paper proves a local finite theorem at modulus 81 for a finite reverse-transport model associated with the 3x+1 map. The result is local and finite in scope: it does not prove global convergence, higher-scale persistence, a forward odd-only bridge, or the global 3x+1 conjecture. The accompanying archive includes: PDF manuscript, LaTeX source, BibTeX file, audit scripts, audit outputs, SHA256 manifest, compile report, and verification report. The computational checks use exact integer and rational arithmetic to recompute the finite objects used in the paper, including the matrix/vector data, residual identities, witness values, dyadic channel checks, and the pairing-law counterexample.

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Cite This Study

Itay Fadida (Mon,) studied this question.

synapsesocial.com/papers/6a1fc5d7dee9eb8c0dce7415 https://doi.org/https://doi.org/10.5281/zenodo.20486127

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