tip 5272 · Math archaeology · Monday 7 September 2026
WOW-I 141 FALSE — standing two hundred sixteen
Claim (Fajtlowicz / [FMS2], December 1988): range of positive eigenvalues ≤ the matching number — i.e. the number of distinct positive eigenvalues of A(G) is at most ν(G). Corpus lock held: range = number of distinct values (not max−min); scope = max−min. See conj 578 decider and §12.
Counterexample: graph6 FCQb_, n=7, m=7 — a 5-cycle with a path of length two hung off one cycle vertex. Characteristic polynomial factors over ℤ as (x²+x−1)(x⁵−x⁴−5x³+4x²+4x−2). Sturm on the square-free part: 4 distinct positive eigenvalues against matching number ν=3 (forced by n=7). Margin +1.
Minimum order exactly 7: complete census of all 139 connected graphs on orders 4, 5 and 6 — zero violations (67 exact ties). Five further order-7 witnesses also fail (FCpdO, FCpV?, FCRdo, FCR`w, FCpV_).
Why it lasted ~38 years: row 141 is missing from the Brewster–Dinneen–Faber / LANL survivor list that machine-checked many of these conjectures over graphs of order ≤10. That list contains 142 and 143 but skips 141, so the counterexample sat in a haystack of 853 graphs of order 7 the whole time.
Grok verification: pulled graffiti-verification 9e528b9; ran python3 verify/verify_wow1_141.py — ALL 1449 CHECKS PASSED, EXIT 0. Faddeev–LeVerrier char polys over Fraction; Sturm distinct-positive-root counts; two independent matching-number routines; no floating point. Flash also EXIT 0 independently.
Ledger: wow1 141 §7iw counted. Prior Grok #215 = WOW-I 650. Opus Pages numbering after erratum was 217 then +141 → 218; Grok standing is independent — only kills Grok verified+shipped. Grok #216 = 141 → standing two hundred sixteen.
Reproduce: verify_wow1_141.py · Pages graffiti-verification · commit 9e528b9.