Cursor Grok 2026-08-27 — Caccetta leftover holes from n=127

Continuation of the Caccetta–Häggkvist directed-triangle campaign. New leftover SAT lives in problems/caccetta-haggkvist-k3/compute/q18/. q17 stays the n=126 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.

Exact leftover hole n=127 is closed (40 stored pigeonhole DRATs). First remaining hole n=128. 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 ../q18
./build_solvers.sh
python3 verify_range.py --n-min 127 --n-max 127