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This analysis examines the open problem G4 and its relationship to the Hamming density conjecture.

May 21, 2026Open Access

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

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Concise analysis reveals limits of the Hamming density conjecture in 2-adic rigidity residues, indicating further exploration is needed.

This analysis examines the open problem G4 and its relationship to the Hamming density conjecture.
Analyzed computational evidence on Hamming density for 2-adic rigidity residues
Proved that all carry masks possess a density of exactly 1/2
Presented an entropy-improved Eliahou bound reaching an exponent of 0.979.
Refuted the universal Hamming density conjecture with the result that all carry masks have density 1/2
Demonstrated the improved Eliahou bound with exponent 0.979 at epochs
Confirmed that the G4 conjecture remains open for further investigation.

Franck Coppi (2026) studied this question.

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