Leftover exact holes from n=109

After the q4 pigeonhole certificates through n=108, the remaining exact orders not implied by Hoàng–Reed or by HKN 0.3465 (nor by the stored F₄ certificate at 0.34640) begin at n=109, δ⁺=37.

A d-outregular oriented graph on n vertices has n d arcs, so some vertex has in-degree at least d. Relabel that vertex as 0. The exact statement reduces to cubes k=|N⁻(0)| ≥ d.

Those cubes are UNSAT, with stored DRATs, at every leftover order through n=114. After n=72 the leftover n are consecutive. 213 stored proofs in this folder (34+35+36+35+36+37). The first remaining hole is n=115, δ⁺=39.

The numerical threshold is unchanged: c = 0.34640 (CKLS 2015 fork). It does not beat 0.3388.

encode.py is the q1 sequential-counter encoder. Replay:

./build_solvers.sh
./run_all.sh

The encoder is not empty: n=21 d=6 is SAT with a checked C₃-free model. High-k cubes empty by a 2-cycle covering count on N⁺(0). Oversized kissat proofs are replaced by drat-trim core lemmas that still replay.