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

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One-flip leftover of the three q11 followup certificates

The recorded finite handle is every unimodular diagonal flip of the three q11 followup certificates, followed by every sign change of Hamming weight at most three. Those three schemes were produced by the q11 followup and were never used as one-flip seeds. The baseline is the 2,415 nonempty degree-eight T-curve schemes already certified (2,367 published, seventeen parent additions, the q8 scheme, nine q9 schemes, thirteen q10 schemes, and eight q11 schemes).

All 93 leftover balls finished (1,416,018 evaluations). No scheme outside that 2,415 appeared. That finished neighbourhood is not a new lower bound. Neither of the two open maximal deep nests is decided.

The claim is an existence predicate that this leftover did not establish. From the repository root, replay the controls and the leftover coverage with:

python3 problems/hilbert16-degree-8/compute/q12/controls.py
python3 problems/hilbert16-degree-8/compute/q12/coverage.py
python3 problems/hilbert16-degree-8/compute/q12/collect.py

This needs Python 3, a C compiler and rustc, with no Python packages to install. run_all.sh exits zero only if a certificate outside the 2,415 exists; a missing certificate is a failure.

lift_candidate.py can repeat a lifting solve with SciPy; those packages are unnecessary here.