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G4 Analysis: What the 2-Adic Approach Proves and What It Cannot — Extended Version with Full Proofs

Year: 2026

Type: preprint

Abstract: Extended technical version of the analysis of Open Problem G4 in the Collatz conjecture. This paper contains the complete proofs of the main results: All carry masks \(C_j = -3^{-(j+1)}\) have Hamming density exactly 1/2 (proved using the Lifting The Exponent Lemma and bitwise complementarity). This definitively refutes the universal Hamming density conjecture. Entropy-improved Eliahou bound reaching exponent 0.979 at continued-fraction epochs. Step-height exclusion for shapes with \(a_i \ge 3\). This is the detailed companion paper to the concise main version.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.20266685

Author: Coppi, Franck

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7161579035

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