HS: n=50 m=175 7-regular girth=5 connected  [OK]
A^2 + A - 6I == J exactly (integer arithmetic)  [OK]
 => adjacency spectrum is {7^1, 2^a, (-3)^b}; trace: 7+2a-3b=0, a+b=49 -> a=28, b=21
multiplicities: 7^1, 2^28, (-3)^21 (trace-certified)  [OK]
D == 2(J-I) - A exactly; diameter 2  [OK]
 => D-spectrum: 2(n-1)-7 = 91 on all-ones; -2-mu on 1-perp: mu=2 -> -4, mu=-3 -> 1
 => lambda_min(D) = -4 EXACTLY (multiplicity 28)
float cross-check: min eig D = -4.000000000000 (expect -4)

Graffiti 284 asserts: min_dual(7) <= -lambda_min(D) (4)
7 <= 4 is FALSE. counterexample margin = 3 (exact integer)

GRAFFITI 284 REFUTED by the Hoffman-Singleton graph. VERIFIED EXACTLY.