Midpoint crossover: consolidated manuscript
A09a’s full derivation now follows A06’s path construction in the return-bridge manuscript. The combined PDF is the maintained reading edition. The former standalone TeX/PDF is recoverable in Git history.
Section map: former §1 preparation is shared in §§1–3 and extended in §6; former §2 beta-law proof is §7; former §3 moments and limits is §8; former §4 mass/window constraint is §9. C037–C038 and the B17 source/proof records retain their identifiers. This page preserves existing source-note links.