Hilbert 16(a) degree 8, q5, 2026-08-29
Grok 4.6 on the existing problems/hilbert16-degree-8 folder,
starting from origin/main e6fe948 (q4 wrap merged). Stopped on
request before either leftover neighbourhood finished.
Record
Re-fetched arXiv:2602.06888: still v3, 27 Jul 2026, 2,367 nonempty degree-8 T-schemes. Bound still ≥ 2,384. Leftover ranks 22–26 and the depth-3 three-split finished on main.
Bound
Has not moved. No q5/certs/new_schemes.json. No candidate reached
python3 verify_new.py. Incomplete search is residue, not a lower
bound. ATTACK.md and the README Problems row are unchanged.
What finished
Nothing in the leftover pair. The q5 stack itself (parent 17,
Rokhlin check, bow-tie probe, skip-prefix check) is what
sh q5/run_all.sh replays.
The size-5 count 37,632,123 and the three first-index cuts live
under compute/q5/certs/. That file is a count, not a scheme
search.
What is incomplete
Odd collections of size 5: three first-index shards, stopped by hand. Combined last progress 18,340,000 evaluations of 37,632,123 tuples. Same twelve published M-schemes as the finished size-4 sweep. Zero nest hits. No shard printed complete.
| shard | last evals | first-index | schemes | hits |
|---|---|---|---|---|
| [0, 11) | 6,140,000 | finished a=0 and a=1; stopped in a=2 | 12 | 0 |
| [11, 32) | 6,120,000 | finished through a=19; stopped in a=20 | 12 | 0 |
| [32, 189) | 6,080,000 | finished through a=44; stopped in a=45 | 8 | 0 |
Pinned even-split BFS remainder (no giant pickle): last printed line walked 4,754,000, remainder evaluations 3,554,000 of a 4,000,000 cap, queue 4,619,029 and growing. Four published (19,3) M-schemes, no new scheme. Queue not empty.
Numbers and scheme strings: leftover_wrap.json in this folder.
The two open nests remain: ⟨4⊔1⟨2⊔1⟨14⟩⟩⟩ and ⟨14⊔1⟨2⊔1⟨4⟩⟩⟩.
Scope
The leftover named in the q4 wrap: pinned even-split BFS remainder
and compatible odd collections of size 5. Code in compute/q5/.
Replay:
cd problems/hilbert16-degree-8/compute
sh q5/run_all.sh