Hilbert 16(a) degree 8, q2, 2026-08-27

Grok 4.6 on the existing problems/hilbert16-degree-8 folder, starting from origin/main 6ae8676 (q1 wrap merged).

Record

Re-fetched arXiv:2602.06888: still v3, 27 Jul 2026, 2,367 nonempty degree-8 T-schemes. Parent 17/17 and q1 replay still green. Bound still ≥ 2,384.

Bound

Did not move unless a later certificate says otherwise.

Scope

Radius-1 thicken of the twenty leftover census triangulations of twist-rank 21–26, a three-split ladder on the published (19,3) collections, odd collections of size 4, and a longer pinned even-split walk.

Replay:

cd problems/hilbert16-degree-8/compute
sh run_all.sh
sh q2/run_all.sh
python3 q2/collect.py

Results

Bound still ≥ 2,384. No q2/certs/new_schemes.json.

Rank 21 leftover thicken: 5/5 complete, 482,344,960 evaluations, evals = $46\cdot 2^{21}$ on each, novel empty. problems/hilbert16-degree-8/compute/q2/certs/thick_r1_rank_21.json.

Pinned even BFS, 400,000 collections: five published (19,3) M-schemes, queue left 393,239. Residue. compute/q2/certs/even_pinned.json.

Three-split ladder on the five published (19,3) collections: 2,719,977 evaluations, 30 known schemes, 0 new, 0 hits. Time cap during the last seed. Residue. compute/q2/certs/ladder3.json.

Odd size 4: size 3 replayed 368,936 / 12 schemes. Size 4 snapshot at 40/189, 3,740,056 evaluations, still those 12, 0 hits. Residue. compute/q2/certs/odd_skel4.json.

Ranks 22–26 (15 triangulations) and both open nests remain.