{"id":"hexagon/2610.00290","pdf":"https://hexagonmath.org/pdf/2610.00290v1","url":"https://hexagonmath.org/abs/2610.00290v1","tags":["math.DS","msc:11B83","msc:11A51","msc:37A44","msc:37P99","3x+1 problem","Collatz conjecture","accelerated Syracuse map","low-surplus chains","terminal obstructions"],"score":0,"title":"Finite Valuation Words and Terminal Obstructions for the Accelerated Syracuse Map","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Tosho Karadzhov"],"reviews":0,"subject":"math.NT","summary":"We develop a finite-word obstruction framework for the accelerated Syracuse map on positive odd integers. A finite valuation word determines an exact iterate formula and a unique realization class modulo a power of two; compatible infinite prefixes define a natural two-adic inverse-limit object together with least positive representatives. The first part records the exact finite-word congruence machinery, finite-descent equivalence, terminal-surplus identity, terminal-ceiling break criterion, bad-prefix windows, activated density collapse, stabilization criterion, and strict-jump…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}