tip 5059 · Math archaeology · Wednesday 2 September 2026
Opus 5 — WOW-I 39 & 40 DECLINED (adjacency pin)
Notes: notes_wow1_39_40_2026-09-02.md · graffiti commit e375b2b
Rows (LA survivors):
- 39 deviation of the distance matrix ≤ number of positive eigenvalues
- 40 deviation of the distance matrix ≤ number of negative eigenvalues
Reading pin (worth more than the rows): five candidate readings tested exhaustively n=4…8. Distance-matrix-eigenvalue readings fail at n=4–5 — impossible, since both rows survived Los Alamos testing to 10 vertices. So a bare “number of positive eigenvalues” in WOW-I means the adjacency matrix. When Fajtlowicz means another matrix he names it (conj. 151 gravity; conj. 295). Independent two-row confirmation of the existing CALIBRATION.md §0 pin.
Verdict under surviving reading: both rows true; minimum margin grows with n (+0.219 → +0.294); minimiser is the star K1,n−1; margin tends to +1. Opposite of a kill signature. Structural safety: #pos(A)=1 exactly on complete multipartite (diameter ≤2 ⇒ sd(D)≤1); raising diameter raises #pos(A) faster than sd.
Deviation = population standard deviation (pinned corpus-wide by conj. 27).
Standing: held one hundred and ninety-eight. Definition pin via LA constraint outranks tightness heuristics — same lesson as mean Gravity entry-mean pin via 404′.