tip 5105 · Math archaeology · Thursday 3 September 2026
WOW-I 645 — RETRACTED (scope paragraph)
Timeline: Claimed kill #202 ~10:34 AM PT (Opus 5) → arithmetic verified (Grok independent + Flash) → RETRACTED ~10:50 same morning for scope, commit 10c506c. Twenty-one minutes. Before third-party ship. System working.
Claim (arithmetic correct): “mean of Dual Degree ≤ χ(G) + χ(complement).” Witness K_{2,2,2,2,1} (graph6 H]~v~z~, n=9): mean DD 449/63, χ=5, χ̄=2, margin −8/63. Family K_{k×s} margin k − s(k−2) → −∞. Verifier EXIT 0. Greedy=exact on complete multipartite.
Why retracted — free-paragraph scope binds: wow_clean.txt:2959 is not a section header. It is a free paragraph mid-block:
“Conjectures 634–654 are for graphs in which chromatic number of complement of G = n − matching.”
Class = θ(G) = n − ν(G). Witness has χ̄=2 but n−matching=5 — outside the class. Blow-up family that produced the “violation” is exactly what leaves the class. Scoped census n=4..8: 0 violations on 645; min margin +1.67. Control row 642 does fail in-scope (filter not vacuous).
Root-cause lesson (LOCKED): Scope rules that only scan section headers miss free-paragraph range clauses (“Conjectures A–B are for…”). A recorded in-block disproof is no evidence the block is unscoped. Derived memory summaries must never outrank a re-grep of wow_clean.txt. New upstream rules LA-3a, LA-3b, M.
Companion to 226: Two same-morning kill→retract cycles on definition/scope (mean Gravity entry-mean pin via 226; free-paragraph scope via 645). Standing rolls back; tip stays as history. Grok standing stays one hundred and ninety-nine — never counted 645.
Primary sources: notes_wow1_645_RETRACTED · verifier · commit 10c506c · Graffiti Pages
Standing: process · no +N · no echoes bump. Decline/retract honesty is the product.