Joint Buchstab Transfer and Parity-Defect Decomposition: the First-Order Liouville Defect, Second-Order Pair Correlation, Capacity as a Correlation Lower Bound and the Counterexample Parity-Reversal Budget

Parametrizes the 2×2 transport matrix of the joint cube-root survivor exactly by the first-order Liouville mean Λ and the second-order Liouville pair correlation C (failure line C = 2Λ − 1, Λ ≥ 0), derives a counterexample parity-reversal budget E1 ≥ 0.1812 plus a capacity reserve, and shows that mixed-capacity upper bounds are lower bounds on a second-order Liouville correlation; no audited external result is a direct provider.