q1 — leftover maximal-stratum thicken and the (19,3) row
The published census is 2,367 nonempty degree-8 T-curve schemes
(arXiv:2602.06888 v3, §5.3). Seventeen more sit in
../certs/new_schemes.json, so the lower bound in this folder is
2,384. This campaign finishes the whole-stratum thicken that stopped
at 4 of 164 census triangulations, walks even Harnack splits along the
occupied (p, n) = (19, 3) depth-3 row (the two open M-schemes live
there), and looks next to the 237 twenty-oval certificates.
Replay
From problems/hilbert16-degree-8/compute:
sh q1/run_all.sh
That re-checks the seventeen, compiles q1/thicken, and diffs it
against the parent thickc on a rank-6 triangulation.
Searches
From the same directory, after python3 prep.py and cc -O2 -o zonec zonec.c
and cc -O2 -o ballc ballc.c:
gcc -O3 -march=native -o q1/thicken q1/thicken.c
python3 q1/thick_drive.py <w> 2 20 q1/thick_out 1
python3 q1/even_walk.py bfs q1/even_out/bfs.jsonl 200000
python3 q1/nest_walk.py <w> <seed> 400 q1/walk_out 12
python3 q1/m2_drive.py 4 q1/m2_out <w> 2
python3 q1/collect.py
A new scheme is a T-curve only after python3 verify_new.py q1/certs/new_schemes.json.
An incomplete search is not a lower bound.
What this run found
The bound did not move. The seventeen still verify; nothing new appeared.
Finished, with certificates under certs/:
- Radius-4 balls around all 237 twenty-oval census certificates (38,920,377 evaluations).
- Compatible odd Harnack-split collections of size at most 3 (368,936 evaluations; twelve known M-schemes).
- A 200,000-collection even-split walk that never drops an odd split (only the five published (19,3) M-schemes).
- The one-split add/drop/swap neighbourhood of every published 22-oval collection (28,861 evaluations; the same 38 M-schemes and nothing else). The two open nests are not one move from any published M-collection.
The leftover whole-stratum thicken (radius 1, rank at most 20) is finished: all 164 leftover triangulations, 1,438,512,000 evaluations. Every scheme outside the published 2,367 is already among the seventeen. The two open (19,3) nests were not on that neighbourhood.
Also finished: radius-6 balls around the eleven of our seventeen certificates whose ball leaves the old swept region (0 novel); the two-split ladder around all twelve published depth-3 M-collections (0 new). Hilbert 16(a) degree 8 is still open.