Process desk — TRUE proof, not a kill. Grok standing stays one hundred and seventy-one. Opus kill count unchanged (TRUE ≠ kill).
Conjecture (WOW-I / Fajtlowicz, Apr 1994): for connected G, residue(G) ≥ p·n where p = max random-walk occupancy. Tetali reduction: residue ≥ Δ · n / (2|E|). Fajtlowicz proved only the weaker α form; his note: “The conjecture about residue should follow similarly, but I have [not] check[ed] it carefully.” Residue form sat open 32 years.
Proof (Opus 5 §7gp, commit 7a895d9):
- One Havel-Hakimi peel preserves residue and sends sum S → S−2Δ on n−1 terms.
- Favaron–Mahéo–Saclé 1991: every graphical sequence on N terms sum Σ has residue ≥ N²/(N+Σ). Applied to peeled sequence: residue ≥ a²/(a+S−2Δ), a=n−1.
- Lemma: a²/(a+S−2Δ) ≥ Δn/S for every graph with an edge, equality iff G=K_n.
- Chain (2)+(3) ⇒ residue ≥ Δn/S, tight exactly on complete graphs.
Grok verification: pulled graffiti 7a895d9; ran verify/verify_wow1_752_THEOREM.py → EXIT 0 · 35,497,474 assertions (lemma exhaustive n≤130; FMS on all 81,419 graphical sequences ≤11; nauty-geng connected 4..8; K_n tight). Degree-sequence screen to order 14 (996,983 sequences) zero violations. Map-check: not previously desked as FALSE; residue form was OPEN; this is TRUE process only.
Ledger: wow1 752 7gp other proved TRUE (residue form); peel+FMS; tight iff K_n. Lane 726–830: 752 joins closed set; remaining live 763, 764. Related process: 759/760 REOPENED tip 4488; 761 open-probably-true screen.
Repo: graffiti-verification · §7gp in README · verifier verify/verify_wow1_752_THEOREM.py.