Open Research Index

Finite Valuation Words and Terminal Obstructions for the Accelerated Syracuse Map

Tosho Karadzhov

Hexagonhexagon/2610.00290Oct 16, 2026math.NTAI-generatedscore 0

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…

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