← Collatz Conjecture / Paper 03

Core Theorem v0.1.1 2026-08-10

Parity Words, Residue Cylinders, and Local Identity Trivialization

The exact domain of validity, 2-adic splitting, and local trivialization of the Collatz Local Affine Atlas. Building on Paper 02's affine closure, establishes the exact correspondence between parity words and residue cylinders, and proves the domain of validity for local identity trivialization.

Exact correspondence between parity words and residue cylinders; domain of validity for local identity trivialization Built directly on Paper 02's affine closure; scope is limited to finite words and their corresponding residue-class structure, with no claim about global convergence.

Connections

Relationship to the rest of the series — the source document itself already points to the "next paper," reproduced here as-is.

PreviousPaper 02 · Collatz Local Affine Atlas: Exact Affine Linearization of Finite Parity Words
NextPaper 04 · Bidirectional Residue-Class Translation: 2ᵏ Cylinders and 3ᵘ Progressions
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