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

Grok 4.6 on the existing problems/hilbert16-degree-8 folder.

Record

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

Bound

Did not move. No new T-curve scheme.

Finished

• Radius-4 balls around all 237 twenty-oval census certificates.
• Odd Harnack-split collections of size at most 3.
• Pinned even-split BFS (200,000 collections; queue not exhausted).
• One-split neighbourhood of all 38 published M-collections: those 38 schemes only.
• Nested odd pairs on the five published (19,3) collections. The a=10 nest admits no compatible nested odd pair.
• Radius-1 thicken of every leftover census triangulation of twist-rank at most 20 (164/164, 1,438,512,000 evaluations). Only rediscovery of schemes already among the seventeen.
• One-split neighbourhood of all 38 published M-collections, and the two-split ladder around all 12 depth-3 M-collections.
• Radius-6 balls around the eleven of our seventeen certificates whose ball leaves the old region.

Replay:

cd problems/hilbert16-degree-8/compute
sh run_all.sh
sh q1/run_all.sh
python3 q1/collect.py

Hilbert 16(a) in degree 8 remains open. The leftover thicken of all 164 rank-at-most-20 census triangulations is finished and added nothing. The two open deep nests are unfinished. The twenty census triangulations of rank 21–26 were never in that leftover.