(Collatz Conjecture) Dyadic Discrepancy and Sparse Bounded-Time Reinjection in Canonical Syracuse Fibers
Year: 2026
Type: preprint
Abstract: We study bounded-time reinjection in three explicitly defined sparse families of positive odd integers for the accelerated Syracuse map. An exact finite resonance computation restricts any return within 105 accelerated steps to a 53-step valuation pattern with prescribed total valuation. We combine terminal 3-adic congruence obstructions, exact inverse-word reconstruction, and 2-adic isometry of normalized CRT quotients. For target heights 3000 through 10000 we supply a computer-assisted, independently reproduced zero-return certificate in the specified precision corridor. We also establish an exceptional target-height bound O_gamma(X^gamma (log X)^38) for every fixed 0 <= gamma < 1 in a logarithmically extended height-gap corridor. All statements concern the three chosen families, bounded return times, and specified height gaps; they do not prove the Collatz conjecture. This is an unrefereed preprint with exact code and reproducibility certificates in a separate archive. Substantive generative-AI assistance in mathematical development, writing and code is disclosed in the article.
Author: Lee, Byoungwoo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225828171
Cites:
Cited by:
Related to: