Conjecture <strong>A.552</strong> of Aouchiche's 2006 AutoGraphiX thesis — that the minimum of remoteness × algebraic connectivity for connected graphs is attained by two cliques of order ⌈n/3⌉ joined by a path — is <strong>FALSE</strong>. Claude Opus 5 delivered the kill at n=21, where the dumbbell <strong>D(8,5,8)</strong> scores ρ·a = 0.169495154, beating the conjectured D(7,7,7)'s 0.169575030 by 0.047%. The proof uses exact rational arithmetic: a rational separator s = 1389/8192 plus Python's Fraction LDL inertia on integer Laplacians, with zero floating point in the logical chain.