A new degree-eight T-curve scheme

Number of nonempty degree-eight T-curve schemes ≥ 2,385. The new scheme is ⟨3 ⊔ 1⟨3⟩ ⊔ 1⟨12⟩⟩, with twenty ovals. It improves the notebook's 2,384 baseline by one and the 2,367 schemes in Geiselmann et al., arXiv:2602.06888v4, by eighteen in total. Neither preferred maximal deep nest is decided.

The interrupted session left a claim, route notes and two source files, but no completed search output. GPT-6 Astra resumed that work, replayed the published archive and seventeen prior additions, and completed the search driver and its independent Rust verifier. The search stopped on its first candidate after 82 of 1,190 planned balls, 1,248,532 sign evaluations. There were 807 observed schemes; only one was outside the baseline.

The old lifting did not support the flipped mesh. A projection method also failed to obtain a lifting. A linear feasibility solve then found integer heights, and exact arithmetic verified every strict inequality with minimum slack 4. This is a useful example of why a failed numerical search is not a nonexistence result.

Validation completed:

• The parent replay passes all published certificates, the seventeen additions, and its existing controls.
• Python and Rust independently verify all 2,384 baseline schemes and the new certificate.
• Positive, rejection and forced-discovery controls pass, including 1,036 independently enumerated sign assignments on a flipped mesh.
• q8/run_all.sh exits zero for the new certificate.
• A fresh replay reproduces every frequency in all 82 saved balls.
• Repeating the optional lifting solve reproduces the exact committed certificate.

The construction, claim, verifiers and retained search prefix live in compute/q8. Replay requires Python, a C compiler and rustc; numerical packages are needed only to repeat the optional lifting search. The hunt used one worker; the discovery run's peak resident memory, including its compiler child, was 45,552 KiB. Search stopped on certification, leaving 1,108 balls unsearched. Covering was not changed.

The PR is to remain unmerged.