# Verification report

The manuscript's accepted scope is a dependent real-power preservation theorem, the exact defect-transport identity, free-compression preservation, the interval classification for symmetric free Lévy unimodality times, and sharpness through the onset of the cited Cauchy/atom mixture. The essential transform inequality is attributed to Anonymous, DOI 10.5281/zenodo.22649756; its unrefereed status is explicit in the abstract and text.

The analytic self-audit checks nonvanishing before each reciprocal, the quadrant of the power subordination map, extension from finite mixtures without moment assumptions, fixed-mode weak closure, and the distinction between strict Cauchy-smoothed monotonicity and weak unimodality of the limiting law. The onset argument uses weak continuity only for a freely infinitely divisible semigroup. Since its unimodal-time set is upward closed and relatively closed, a nonempty proper set has a positive attained endpoint. Rescaling that endpoint gives the sharp-range law, without claiming a computed density.

The accompanying check_power_transport.py verifies five exact symbolic identities. Both normal and optimized Python modes must agree, and the deliberate transport-coefficient corruption must be rejected in both modes. The archived earlier source audit separately contains 13 reconstructed algebra identities, four power identities, 1,200 seeded 70-digit mixture tests per interpreter mode and two rejected corruptions. These finite and symbolic checks do not replace the analytic arguments.

Final package readiness requires a successful built-in LaTeX check, a warning-free saved PDF, visual review of every final page, byte-verified source ZIP, and matching artifact hashes. Machine receipts and the package manifest record those completed checks; this report is not itself a receipt.

This note is self-audited, AI-assisted and unrefereed. No independent human review, proof-assistant verification or absolute priority is certified. It does not claim a newly authored solution of the original pairwise AIM problem. Public release on Zenodo or EulerSolve does not change those qualifications.