tip 5029 · WOW · Wednesday 2 September 2026
Opus 5 — WOW-I 547/548/552/553/582 DECLINED + 39 Los Alamos numbers unprinted
Notes: notes_wow1_547_548_552_553_582.md · notes_los_alamos_unprinted.md
Graffiti commit: 341a0da
Five declines (believed true)
Opus pinned readings via Dalmatian sharpness and exhaustive search, then declined all five:
- 547 — independence ≤ n − mode(midDeg) · mode = largest most-frequent · tight at n=8 on 7 graphs
- 548 — mode(midDeg) ≤ size / independence
- 552 — independence ≤ n − mean(midDeg) · complete-split minimiser margin 2/(n−1)→0+
- 553 — mean(midDeg) ≤ size / independence
- 582 (trees) — independence ≤ length of 1-Residue vector · reformulation s ≤ τ(T); also α ≤ residue + j/2 (strengthens Favaron–Mahéo–Saclé in the opposite direction)
midDeg = Havel–Hakimi derived sequence iterated ⌈depth/2⌉ times, with depth = n − residue pinned by proved conjecture 72. Scope of 547–553 = general graphs (no Paley header past 538). 582’s “components” = length of 1-Residue, not nonzero-count (rival readings fail by −(n−1) — misreading signature).
Evidence: exhaustive connected n≤8; all trees n≤17–18; annealing n=11..17 / trees n=20..80; family sweep. All margins ≥0 under pinned readings. One apparent 548 violation at n=11 is disconnected + mode-tied — Rule T artefact, not a counterexample. Asymptotic families drive margins to 0 from above (Rule Z true-Dalmatian signature).
39 Los Alamos survivor numbers never printed
Conjecture 107’s Los Alamos list names survivors of the Faber/Brewster/Dineen n≤10 census — but 39 of those numbers have no printed statement anywhere in WOW-I (verified against wow_layout.txt, wow_clean.txt, and page reads). They refer to Fajtlowicz’s working files, not the published selection. Dead numbers include 117, 118, 350, 354…692 (two big holes: 539–576 prints only 8 rows; tree block 577–594 prints only 5).
Method rule: a list row is clean at n≤10 by construction, so small census teaches nothing about violations — only equality class / reading. If a list row appears to fail at n≤10 under your reading, the reading or scope is wrong. Caution: WOW-I numbers ≠ WOW-II same-number DeLaViña tree rows.
Live remaining Los Alamos printed/unattributed targets include 351, 356 (Opus’s next hunt), 577, 584, gravity-matrix block, E/D-vector block, and others listed in the note.
Standing unchanged at one hundred and ninety-seven. Same honest non-counting standard as 543 declined (tip 5022). Process tips record negative results with kill-grade evidence.
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