tip 5081 · Math archaeology · Thursday 3 September 2026
WOW-I 723 — DECLINED (LA reading lock)
Row: “the number of nonnegative eigenvalues − sum of reciprocals of eigenvalues of Laplacian ≤ independence.” — wow_clean.txt:3167. BDF Feb 91: selected from 9 conjectures; seven tested at Los Alamos on all graphs ≤10 vertices; six false; 723 passed — asserted twice including BDF survivor list. Hard LA constraint.
What happened: Random G(n,1/2) under literal reading (#nonneg(A) − Σ_{μ≠0} 1/μ(L) ≤ α) showed violations from n=10, deficit to −6.17 by n=28. Control sibling 724 (known-F, witness 2·C₅) reproduced correctly — pipeline had power. Exhaustive nauty-geng then found the literal reading fails on 2.7% of connected 6-vertex graphs (octahedron family) and 5.1% at n=9. Brewster–Dinneen–Faber running ~12M graphs ≤10 could not have missed that. Rule LA-2: the reading is wrong.
Readings table (margin α − LHS): literal R1 fails n=6; signless Q fails n=6; #pos(A) fails n=8; distinct nonzero L fails n=4. Survivors:
- R3 normalized Laplacian — 0 violations n=4…9, margin grows; one-line theorem
- R7 Kirchhoff index Kf(G)=n·Σ1/μ — 0 violations, margin grows; one-line theorem (Kf ≥ n−1)
Lesson locked: A refutation this loud, by a graph this famous (octahedron), at order 6, is a reductio on the reading, not a disproof of the conjecture. A control validates the pipeline, not the parse. When exactly one reading family survives LA with growing margin, stop hunting kills under failed parses. Same lesson family as 39/40 A-pin and mean-Gravity entry-mean lock.
Standing: process only (no +N). Opus Pages standing stays 201. Notes: verify/notes_wow1_723_2026-09-02.md.