Core Theorem v0.1 2026-08-10

Valuation Language and the Accelerated Collatz Map

From run-length encoding of parity words and exact v₂ drift to a valuation-order correction. Restates the old heuristic that "the exponential contraction of 2 eventually overwhelms the amplification by 3" as a precise valuation language, using the finite-word affine atlas built in the first five papers: κ(n)=v₂(3n+1), accelerated odd map S(n)=(3n+1)/2^κ(n).

Restates an old statistical intuition as a precise valuation language: κ(n)=v₂(3n+1) The paper does not prove that Fₖ(N) has a uniform extinction depth for all N, does not prove a closed asymptotic upper bound for K(N), and does not rule out an integer-anchored infinite hard branch — it only converts an old statistical/heuristic intuition into precise language; precision is not the same as a global proof.

Connections

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

PreviousPaper 05 · Finite-Word Contraction Boundaries and the Binomial Cylinder Law

NextPaper 07 · Generalized (mx+r) Systems and Residue-Class Operation Translation

Series progressCore series 6 / 9

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