[Tuafo]

This package closes below-nine fitting compression for both the selected P111 bit-supplier graph and the pinned P112 graph, at every block size. Every fitting matrix with invertible d-by-d diagonal blocks has rank at least 9d over every field; the inherited binary construction attains 9d in characteristic two. Even nonlinear zero-error codes for d-bit messages require exactly 9d broadcast bits.

A source-pinned 14-vertex witness is four isolated vertices plus Petersen in the usual fitting/side-information convention. A coordinate reflection embeds the same witness directly in the selected PR589 P111 labels; this is checked from the raw inputs, without assuming P111 is a subset of the chosen P112. A separate four-clique argument proves the characteristic-two result directly. An exact 113-term rational certificate replays the known Petersen lower bound five, followed by documented row-space and entropy reductions. Petersen's rate is credited to Blasiak–Kleinberg–Lubetzky, Fact 5.6(1); the binary E8/symplectic upper construction is credited to Leung et al. and Peeters. No novelty claim is made for those known results.

Validation: all three registered Python 3.12 verifiers pass under -I -B -O with no third-party dependencies. They check the two source pins, 2,912 and 2,870 required-zero pairs, 12,544 and 12,321 binary Gram entries, exact induced-graph isomorphisms, all 1,024 rational dual coefficient sums, a matching positive fixture, and 21 corruption controls. Metadata/source pins and git diff --check pass. A separate AI implementation independently corroborated the P111 reflection, graph and full binary rank. These are finite certificates plus written proofs, not proof-assistant formalization.

This is a side result of the helper-inventory investigation: no native word, paid supplier improvement, selected-frontier change, or multiplication-exponent gain is claimed. The next useful question must change the graph/interface constraints or save other paid work. Base/source commit: 0b1cccf. Scope, source hashes, replay commands, limitations and inherited input attribution are in the package. The selected P111 word retains the PR589/555/543/545 lineage; its inputs are unchanged.

Coordination: #1713. Complete overlap refresh at 2026-10-14 10:16 UTC covered 460 open PRs and 435 Discussions including comments/replies; no matching new P111 claim was found, which is not a novelty certificate.

Prepared for Thiago with substantial OpenAI GPT-6 Astra and Codex assistance. Apache-2.0; predecessor attribution retained.

[Mister-Meeseeks]

Batch review at 78033981ec296b545b3cb50435668fe98e764e65.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Exact P111/P112 induced four-isolated-plus-Petersen embedding; 113-term rational Shannon/rank dual reconstructed and all-field block-rank/zero-error binary entropy proof reviewed. Lower bound 9d, attained by inherited characteristic-two/binary labels, for this fixed graph only. Independent graph, dual and P111 checks passed; not a supplier cost lower bound or new kappa.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.