q5 — leftover (19,3) nests

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. q1–q3 finished the radius-1 leftover thicken of every leftover census triangulation of twist-rank at most 26. q4 finished the three-split around the twelve published depth-3 M-collections. The two open (19,3) deep nests remain.

This folder continues the leftover named in the q4 wrap: the pinned even-split BFS remainder (queue 1,167,098 after 1,200,000 collections) and compatible odd collections of size 5. It does not re-run leftover thicken or the finished depth-3 three-split.

Replay

From problems/hilbert16-degree-8/compute:

sh q5/run_all.sh

That re-checks the seventeen and the bow-tie collection.

Searches

From the same directory, after python3 prep.py:

python3 q5/even_walk.py bfs q5/even_out/bfs.jsonl 8000000 1200000
python3 q5/odd_skel.py 5 q5/even_out/odd_skel5_0-11.jsonl --minsize 5 --shard 0:11
python3 q5/odd_skel.py 5 q5/even_out/odd_skel5_11-32.jsonl --minsize 5 --shard 11:32
python3 q5/odd_skel.py 5 q5/even_out/odd_skel5_32-189.jsonl --minsize 5 --shard 32:189
python3 q5/write_certs.py
python3 q5/collect.py

The even-split BFS reconstructs the q4 prefix of 1,200,000 collections without re-evaluating schemes, then evaluates the remainder. It does not write the giant seen/queue pickle (that stalls the machine). Complete only if the queue empties. There are 37,632,123 compatible odd 5-tuples (certs/odd_skel5_count.json). Size 5 is complete only if every first-index shard finishes and the shards cover all 189 odd splits. Each shard writes a tiny .next first-index file so a later run can skip finished indices. Sizes at most 4 are already finished (q3/certs/odd_skel4.json).

A new scheme is a T-curve only after python3 verify_new.py q5/certs/new_schemes.json. An incomplete search is not a lower bound.

What this run found

Stopped before either leftover neighbourhood finished. No certs/new_schemes.json. The bound stays 2,384.

Odd size 5: three first-index shards, last progress 6,140,000 / 6,120,000 / 6,080,000 evaluations of 12,700,937 / 12,394,262 / 12,536,924 tuples. Combined 18,340,000 of 37,632,123. The union is the same twelve published M-schemes as the finished size-4 sweep. Zero hits on the open nests. No shard completed.

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 still growing. Four published (19,3) M-schemes only. The queue did not empty.

An incomplete search is not a lower bound. A new scheme is a T-curve only after the exact verifier. Numbers: notes/grok-2026-08-29-hilbert16-d8-q5/leftover_wrap.json.