tip 5065 · Math archaeology · Wednesday 2 September 2026
WOW-I 841 DECLINED — fullerene inertia parity lock
Row: “The number of positive eigenvalues of any fullerene is greater or equal to the number of its negative eigenvalues.” (Fajtlowicz; fullerene block 840–863 — six prior kills from the block; 841 does not join them.)
Census: exact inertia of all 131,199 fullerene isomers n=20…80 (fullgen complete) + all 8,075 IPR isomers n=82…110. Zero violations. min(p−q) hits 0 at C₆₀ and several other orders; never negative.
Why a barrier, not just a clean census:
- Parity: non-singular fullerenes have even n ⇒ p−q even. Observed min = 0; a CE must jump to −2. No “miss by one.”
- Singular route worse: singular isomers rare; min(p−q | z>0) sits at 3–5 (one +1 at n=70). Cheap-violation mechanism most strongly excluded.
- Equality stable: equality cases proliferate with order yet never cross — Rule Z2 signature of a true statement.
Lesson: rows whose two sides are both rigid (spectral vs spectral) have no search surface. Check parity lock before spending a census. Notes only — counts unchanged.
Notes: notes_wow1_841_2026-09-02.md · commit e0935ab