Cube index for exact Caccetta–Häggkvist triangle leftover orders n=73 through n=108 (1026 cubes). First remaining hole n=109. The DRAT bytes are not in the git tree; see ../../STORAGE.md.

A d-outregular oriented graph has n d arcs, so some in-degree is at least d. Relabel that vertex as 0. The exact statement reduces to cubes k=|N⁻(0)| ≥ d. Each cube was UNSAT with a DRAT. Local replay regenerates the CNF from encode.py and checks a regenerated proof; do not trust leftover certs/*.cnf scratch files.

cd problems/caccetta-haggkvist-k3/compute/q4
./build_solvers.sh
./run_all.sh

The index is replay.json after a successful verify_keep.py. Circulant soundness (cyclic degree, not a counterexample) is soundness_n73_d24.json.

A separate F₄ flag-algebra certificate with the CKLS 2015 fork (c = 0.34640) is f4_or_new_certificate.json. Replay:

python3 verify_q4_certificate.py certs/keep/f4_or_new_certificate.json

Independent F-coordinates (no import of that verifier):

python3 dump_f_coords.py

writes f_coords_0.3464.json.