Cursor Grok 2026-08-28 — Caccetta leftover holes through n=137

Continuation of the Caccetta–Häggkvist directed-triangle campaign. New leftover SAT lives in problems/caccetta-haggkvist-k3/compute/q28/. q27 stays the n=136 store. q4 stays the n=73–108 store and the F₄ certificate.

Published unrestricted threshold is still HKN 0.3465 (arXiv:0908.2791v4, Theorem 1.2). Do not treat 0.3388 as published.

Leftover n=137 is closed: d=46, cubes k=46..89, 44 stored DRATs after drat-trim -l (largest core k=46, 13.0 MB). Independent python3 verify_range.py --n-min 137 --n-max 137 reports 44 checked, 0 failures. Parent F₄ at 0.34645 and the q4 CKLS-fork certificate at 0.34640 both still replay. Encoder regression (including n=21 d=6 SAT and cyclic soundness at n=73 d=24) is 0 failures.

n=138 is not stored. Residue, not a bound. F₄ unchanged at c=0.34640. Did not beat 0.3388. The conjecture 1/3 is open.

Replay:

cd problems/caccetta-haggkvist-k3/compute
python3 verify_certificate.py certs/f4_certificate.json --margin 0.05 --c 0.34645
cd q4
python3 verify_q4_certificate.py certs/keep/f4_or_new_certificate.json --margin 0.05
cd ../q28
./build_solvers.sh
python3 verify_range.py --n-min 137 --n-max 137
python3 regression.py