Cube index for exact Caccetta–Häggkvist triangle orders from n=38 through n=72. 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/q3
./build_solvers.sh
./run_all.sh

Orders stored: 38, 39, 41, 42, 44, 45, 47, 48, and 50 through 72. The n ≡ 1 (mod 3) values 40, 43, 46, 49 are already implied by HKN 0.3465. The index is replay.json after a successful verify_keep.py. Circulant soundness (cyclic degree, not a counterexample) is soundness_n38_d12.json.