q7 — leftover (19,3) nests

The current paper record is 2,367 nonempty degree-8 T-curve schemes (arXiv:2602.06888 v4, §4.3). Seventeen more are independently verified in ../certs/new_schemes.json, so the lower bound in this folder starts at 2,384. The two algebraically open (19,3) deep nests remain the main targets.

q5 left two incomplete searches: 18,340,000 evaluations from the 37,632,123 compatible odd collections of size 5, and a pinned even-split BFS whose queue was still growing. This folder finishes the odd first-index space in C rather than resuming Python shards, and replaces the even BFS with direct fixed-odd component counting and enumeration. It never writes a multi-gigabyte seen/queue pickle.

Replay

From problems/hilbert16-degree-8/compute:

sh q7/run_all.sh

A candidate is a T-curve only after

python3 verify_new.py q7/certs/new_schemes.json

accepts its primitive regular triangulation, exact lifting, signs, and independently recomputed scheme.

Long searches

sh q7/run_leftover.sh

The odd search is complete only when its aggregate certificate counts all 37,632,123 size-5 collections. The even search records exactly which fixed-odd components finish. The a=10 component has 126,336 collections; the nested-box a=17 component has 25,292,736. The other nonempty-odd components are larger than 10^10 and are counted, not enumerated. Any unfinished component is search residue, not a lower bound or an obstruction.

What this run found

Odd size 5 finished 37,632,123/37,632,123: twelve published M-schemes, neither open nest. The a=10 and a=17 even components finished on known (19,3) schemes. Further enumerable even components of published M-collections, including the (7,15) neighbour of ⟨5⊔1⟨6⟩⊔1⟨9⟩⟩, likewise stayed on known schemes. No certs/new_schemes.json. The bound stays 2,384.

The leftover Harnack / Wiman / ⟨17⊔1⟨1⟩⊔1⟨2⟩⟩ even components remain unenumerated (counts 8.8e10, 2.5e11, 2.0e11). Incomplete search is not a lower bound.