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research: Yu–Oh χ=4 fixture with unit pivots 12 and full box 13 - #3454
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The released question in PR #2890 asks for an admitted rank-three zero digraph with dichromatic number at least four, and asks whether such a coloring obstruction actually obstructs the full anchor box. This package instantiates the established Yu–Oh thirteen-ray configuration and separates the answers: χ(Z)=4, matched canonical unit-pivot maximum 12, full directed anchor-box value 13.
The proof admits the integer coordinates into the rational three-total model, reduces three-color impossibility to eight face orientations, supplies a compatible twelve-row unit witness, and constructs a thirteen-row general witness using two face blocks and seven odd-tie middle rows. The replay independently checks coloring, all 5,184 pivot maps, both retained witnesses against the literal definition and the frozen PR #3393 oracle, and semantic/source failure controls.
Validation: both registered CPython 3.12.15 commands passed, including isolation, optimization and warnings-as-errors; metadata and post-commit source-history checks passed. Canonical main and fork main were refreshed and the branch rebased before submission.
Attribution: the graph and rays are due to Sixia Yu and C. H. Oh, arXiv:1109.4396v1, visible equation (1), PDF page 2. This is a repository instantiation, not a new graph or discovery of its chromatic property. Aaron Wang/navinor's PR #2890 question and DreamingOfClouds's F-star lineage retain credit. Written by Sagar Thakrar with substantial OpenAI Codex assistance; same-session agents supplied proof, controls and review.
Scope: exact thirteen-row fixture only. It does not contradict PR #2890's bounded searches, resolve the all-even twelve-line case, establish a general F-star theorem or counterexample, or change the selected frontier. The literature PDF and predecessor search are not replay dependencies. Open next questions are in the package.
Package:
research/fstar-yu-oh-zero-digraph/. Coordination: claim and final handoff.