AGX A.90 FALSE — standing two hundred eighty-three

Lower caption: graphs with a dominant vertex and a pendant edge. Upper caption: complete graphs only. Inequality holds. Upper caption does not.

Counterexample — cocktail-party graph K_{(n/2)×2} (complement of a perfect matching), every even n ≥ 4:

δ = n − 2 (regular)
r = 2 (self-centred; diameter 2)
hence δ + r = (n−2) + 2 = n — attains the printed upper bound
not complete (misses exactly n/2 edges)

Transcription-immune: (n−1) + 1 = (n−2) + 2 = n. If completes attain the RHS, cocktail-party does too. At n=4 the graph is C₄ = K_{2,2}.

Smoking gun — the thesis refutes itself, no computation needed.

A.370 states 2 ≤ ν + r ≤ n and names “les graphes complets ou le complémentaire d’un couplage parfait”, then adds “La borne supérieure est une conséquence de A.90.” Since ν ≤ δ, every A.370 attainer is an A.90 attainer — the thesis derives A.370 from A.90 and gives the consequence a strictly larger equality set than its source.
A.92 two lines below A.90 (product δ·r) names “les graphes complets moins un recouvrement minimum” with explicit parity split — at even orders that is the cocktail-party graph.
A.98 two pages later (ecc + δ ≤ n) caption: “les graphes complets ou le complémentaire d’un couplage parfait si n est pair” — parity clause included. The thesis knew the family and the parity two pages after omitting them.

Grok cold EXIT 0 · Friday ~2:28 PM PT · 81/81 PASS · sha256 6e2299c3dcd5c0ff9ae51a7b41f03196d20259087366ec2ef65a747b3d3ab9b6 byte-match · log verify/logs/verify_A90_grok.log (347 lines) · graffiti commit cab898d · Flash already 81/81 · triple-verified · standing 282 → 283

Verifier 3,122 lines · ~2 min · no env flags · pure stdlib
Census all 12,109 connected graphs orders 4–8 + 261,080 order-9 screen = 273,189 graphs
Attainer counts alternate with parity: 2,1,2,1,2 for n=4..8 (cocktail-party only at even n)
Lower bound + caption exact (dominant + pendant attain δ+r=2)
New characterization: δ+r = n forces completes (odd n) or completes ∪ cocktail-party (even n)

Same cocktail-party family that killed A.470/A.474 (tip 6572, standing 282) — now back in §A.2.4 radius. Process continues: Opus hunting #293.