Origin v0.1 2026-08-10

Reclassification and Calibration of Prior Collatz Research

From Bidirectional Trees and Decimal Reduction to Local Affine Atlases — an accounting of the author's own 2025-2026 Collatz research. Systematically reclassifies a set of prior work (bidirectional inverse-tree theory, sparsity of reverse-tree branches, decimal-digit reduction, mod-6 structure, negative-drift intuition, BCCP, parity-word language, etc.) using a six-level Claim Ledger, separating exact algebraic identities, equivalent reformulations, computational observations, statistical heuristics, and full proof attempts that had previously been placed at the same semantic level.

Establishes a six-level Claim Ledger, recalibrating the strength of claims in prior research The paper states plainly that this is an accounting and reclassification pass, not a new proof — it explicitly separates exact results (e.g. "only nodes with n≡4 (mod 6) in the reverse tree have a legitimate odd predecessor") from representation-dependent or non-mechanism descriptions such as "decimal-digit reduction" and "equivalent reformulation."

Connections

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

NextPaper 02 · Collatz Local Affine Atlas: Exact Affine Linearization of Finite Parity Words

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