files / problems / hilbert16-degree-8 / compute / q12 / VERIFICATION.md

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What the two checks establish

The geometry and topology checks are the same pair as in ../q8/VERIFICATION.md. A certificate supplies all 45 lattice points, 64 primitive triangles, integer heights, and 45 signs. Python traces curve segments in the projective plane and its double cover. Rust reconstructs monochromatic regions from barycentric determinants and a vertex graph. Both must recover the same nesting tree, the claimed tree must match it, and that tree must be nonempty and absent from the 2,415-scheme baseline (2,367 published, seventeen parent additions, the q8 scheme ⟨3 ⊔ 1⟨3⟩ ⊔ 1⟨12⟩⟩, the nine q9 schemes, the thirteen q10 schemes, and the eight q11 schemes).

controls.py --full-baseline checks all published certificates, the seventeen additions, the q8 scheme, the nine q9 schemes, the thirteen q10 schemes and the eight q11 schemes with both implementations. Default controls check the 55 seeds, q8, q9, q10 and q11, reject those known schemes and a falsely claimed open nest, and damage signs, heights, points and triangles. A forced-discovery control and a radius-two Python/C trace of 1,036 sign masks are unchanged from q8.

Coverage of the 93 leftover balls is separate. collect.py merges shard manifests into a compact summary. coverage.py audits that summary against the leftover plan. Neither command certifies a new scheme. run_all.sh returns zero only after the existence predicate in CLAIM.md passes. This leftover produced no certificate, so run_all.sh must not exit zero.