paper26

Paper XXVI Public Evidence Companion

This directory contains the paper-owned computational companion for Pair-Chain Transfer Operators and Random Synchronization.

Current Boundary

• The exact pair-chain construction, Černý Perron asymptotic, rare-run realization, and reset-word waiting envelope form the new theorem surface.
• The uniform-input Černý mean is a pair-transfer recovery of Gusev's 2014 Bernoulli-input result, not a new formula.
• Theorem A.1 proves the second-order analytic refinement, with gamma_1=0, gamma_2=pi^2/24-3/4, explicit constants N3=64, c0=4, and remainder bound |R3| <= 16*n^3*epsilon^3. The expanded constant verification in u3-proof.md is supplementary and is not a premise of the proof.
• pair_chain.py is the standalone finite implementation; the family producer writes the two paper-owned JSON reproductions under results/.
• Each JSON result distinguishes exact integer/formula fields from bounded float64 spectral observations. The declared replay tolerance is 1e-9.
• The Lean package is a partial formalization of TA-III finite-sum arithmetic and its conditional certificate chain. It does not formalize probability spaces, pair chains, or TA-I/TA-II spectral claims.
• This paper does not imply Forced-FFS, General FFS, or a deterministic Cerny proof.

Run the public-package validator from the repository root:

python experiments/paper26/generate_family_results.py
python experiments/paper26/validation/validate_lean_formalization.py --replay
python experiments/paper26/validation/validate_public_package.py

The validators consume explicit paper-owned inventories. They perform local closure verification and numerical replay; they do not establish independent mathematical validation or replace the manuscript proofs.