Integer core minima: 2147232289/2147483648 (ideal), 1073576721/1073741824 (imperfect); 3240 states freshly replayed. WO joint bound 0.999766315849; finite-fuel F bound 0.991645258049; mixed opposite-pair lower 0.0074873613014. Configured certificate applicable: True; simulated joint event: True. Simulation is illustrative.