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Paper 05
Core Theorem
v0.1
2026-08-10
Finite-Word Contraction Boundaries and the Binomial Cylinder Law
From exact affine drift and a word-order correction to a purely combinatorial account of the 89.4943% figure. Builds a binomial explanation for finite-word contraction boundaries on top of the first four papers' exact affine structure.
A binomial Cylinder Law for finite-word contraction boundaries; a purely combinatorial account of the 89.4943% figure
The paper explicitly 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), does not rule out an integer-anchored infinite hard branch, and does not elevate Pₖ→1 into a global convergence conclusion.
Connections
Relationship to the rest of the series — the source document itself already points to the "next paper," reproduced here as-is.
Series progressCore series 5 / 9