7.2. Methods no longer required🔗

The earlier derivative-and-moment route in mathematical-proof.md remains a mathematical reference. The completed finite-difference route does not need Cauchy estimates for every derivative, boundary moment identities, or absolute integrability of all moments on the boundary half-line. These are not missing hypotheses of the final theorem.

See finite-difference-proof.md for the argument and verification.md for the independent checks. Sharp Five Exponentials and Four Exponentials remain separate research targets; Hardy completion does not resolve either one.