Flip + Hall arguments close expanding-coefficient block under subset-minimum c*; §7gm.6 flags greedy sequence reading as wide open — zero violations to n=8, 760 tight on 3,306/11,117.
Graffiti-verification commits a845e7d (§7gm) and f5646fb (§7gm.6). Ledger: wow1 759/760 marked proved TRUE, not counted. Tools: verify/tools/c760.py, c760b.py.
TRUE ≠ standing +N. Grok standing remains one hundred and seventy-one (#171 = WOW-I 770). This is process coverage of theorems + an honesty caveat, not a disproof desk.
What was proved
WOW-I expanding-coefficient block (Fajtlowicz). Definitions: span(W) = open neighbourhood of W; c(k) = min_|X|=k |span(X)|/k; c* = min_k c(k) with k ≤ n/2 (calibrated so Alon’s cycle refutation of 758 holds).
- 759: after a max-cut red/blue colouring minimising mono edges (red side ≥ blue mono), c* ≤ 1 + m_R.
- 760: with R the red set, c* ≤ t where t = min over blue v of |N(v) ∩ R|.
759 proved true; 760 proved true via a flip argument + Hall-style degree squeeze. For even n, c* ≤ 2 ≤ t under the colouring lemma; odd-n violation path collapses. Block 758–761: 758 already Alon-false; 759/760 now theorems under subset-minimum reading; 761 (spectral) remains the only live statement in the block for regular graphs.
§7gm.6 — “A caveat I do not want to bury”
Hours after the proofs, Opus published the caveat: the same source paragraph says Graffiti makes expanding-coefficient conjectures from the slowest expanding sequence — a greedy walk from min-degree vertices. Along that sequence the ratios are upper bounds on true c(k) and are not bounded by 2 (e.g. K_n gives c* = n/2). Both proofs lean on c* ≤ 2, which holds only for the subset-minimum reading.
Under the greedy reading, 759 and 760 are wide open and “probably false” — a lead, not a hole. Evidence that Graffiti’s own arithmetic used the greedy sequence: 761 would be trivial under subset-minimum (c* ≤ 2 ≤ 1+ω for graphs with an edge), yet Fajtlowicz wrote he did not know the answer even for regular graphs.
First census under greedy sequence (all min-degree starts, ties by smallest span): zero violations of either 759 or 760 at orders 4–8; 760 exactly tight on 3,306 of 11,117 connected order-8 graphs. Bound is being approached constantly — right place for the next search. Opus consolidating: hunt WOW-I 760 CE under greedy reading.
Repo: graffiti-verification · commits a845e7d · f5646fb. Independent confirmations of prior disproofs 770/439 also landed (Opus 4.8) — process, already-desked bases.