(A) finite shift identity: 530 exact checks (+ symmetry/positivity), failures = 0
(B) Lemma-1 inequality on arbitrary configurations: 470 exact checks, failures = 0
(C) Doob-transform and ground-state-transform identities: 40 random networks, failures = 0
(D) r=3/2: 2002 pairs over adversarial patterns; min D'(1+r)/D = 1.666667 (>=1 needed); max c*D^3 = 3.750000 vs K=(1+r)(2+r) = 8.750000; ok=True
(D) r=769/500: 2002 pairs over adversarial patterns; min D'(1+r)/D = 1.650195 (>=1 needed); max c*D^3 = 3.903444 vs K=(1+r)(2+r) = 8.979444; ok=True
