G4 Analysis: What the 2-Adic Approach Proves and What It Cannot — Rise and Fall of the Hamming Density Route

Concise analysis of Open Problem G4. Computational evidence initially suggested a promising universal positive lower bound on the Hamming density of 2-adic rigidity residues rm(a). We prove that all carry masks have exactly density 1/2, definitively refuting the universal Hamming density conjecture. We also present the entropy-improved Eliahou bound reaching exponent 0.979 at epochs. G4 remains open.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-19
DOI
https://doi.org/10.5281/zenodo.20276811
Primary Topic
advanced mathematical theories
Type
preprint
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preprint

G4 Analysis: What the 2-Adic Approach Proves and What It Cannot — Rise and Fall of the Hamming Density Route

Franck Coppi
Zenodo (CERN European Organization for Nuclear Research)
advanced mathematical theories
preprint

G4 Analysis: What the 2-Adic Approach Proves and What It Cannot — Rise and Fall of the Hamming Density Route

Franck Coppi
preprint en

Abstract

Concise analysis of Open Problem G4. Computational evidence initially suggested a promising universal positive lower bound on the Hamming density of 2-adic rigidity residues rm(a). We prove that all carry masks have exactly density 1/2, definitively refuting the universal Hamming density conjecture. We also present the entropy-improved Eliahou bound reaching exponent 0.979 at epochs. G4 remains open.

Zenodo (CERN European Organization for Nuclear Research)
advanced mathematical theories
DOIOpen Access PDFOpenAlex
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G4 Analysis: What the 2-Adic Approach Proves and What It Cannot — Rise and Fall of the Hamming Density Route — Franck Coppi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS