Ternary mutual-information continuity counterexample — written proof v1

Written-proof v1 of an explicit ternary classical counterexample to the general different-marginals mutual-information continuity proposal in arXiv:2408.15226v2, Eq. (106), also v1, Eq. (54).

For every 0 < epsilon <= 1/16, the two actual 3 × 3 joint probability tables have total variation distance exactly epsilon, mutual-information difference 2 h(epsilon) - epsilon log 2, and strictly positive excess h(epsilon) - epsilon log 16 over the proposed bound h(epsilon) + epsilon log 8. Thus the general proposal fails at arbitrarily small distances. As diagonal density matrices, the same tables also supply a commuting quantum example.

Scope and status: both marginals change. The fixed-one-marginal version remains unresolved by this note. Novelty and priority are unconfirmed. This release contains the complete written proof; Lean formalization is incomplete and not certified in this version. No external independent review is certified.

Source is fixed to commit a179e33532707abe09247d87aad484e9965847b4, directory notes/mutual-information-continuity-counterexample/. Source PR #12 contains the isolated addition.

Six assets: paper.md, paper.pdf, paper.tex, mutual-information-continuity-counterexample-v1-source.tar.gz, RELEASE_BINDING.json, and SHA256SUMS_ASSETS. The source archive contains all eight files at the fixed commit, including the full written proof, reproducible TeX/build script, three-page PDF, version manifest and source checksums.

Mechanical verification: both primary equation locations checked; all eight source files read back byte for byte from the fixed commit; all three rendered PDF pages and formulas checked; two builds in separate temporary directories yielded identical PDF bytes. RELEASE_BINDING.json records the exact commit, source-file hashes, publication scope and asset hashes; SHA256SUMS_ASSETS covers the other five assets.

PDF SHA-256: 86f45ddb61649676d8982d351b2958a0d44b2ba9ffcbff6b62f90ff46e4bdfc4.