Ku-Mellin-PATP: reproducibility code

Verification and reproducibility code for the revised version of the paper "Closed-form moment propagation through fractional-power response surfaces via the Mellin transform". Reproduces the exact region-of-validity analysis with the mixed-multi-index counterexample, the Mellin transform of the truncated normal, the confluent (log-power) treatment of the degenerate point alpha = 1/2, the 50-digit re-verification of the manufactured-solution benchmark and the separable 2-D propagation, the balanced benchmark over two response classes, the heavy-tail accuracy benchmark, the engineering example (convective cooling under Weibull wind) and the out-of-sample real-data case study on CWRU bearing records 105 and 106 with a moving-block bootstrap. The scripts of the submitted version are kept. Includes the Lean 4 / Mathlib formalization of the four supporting lemmas.