# CSM_RH Paper 32 v0.1

Campaign 31 reaudits EMBF after the later Lambda-sharp/residual and higher-uniformity developments.

Main results:
- prime-only cumulative error B_theta differs from the Lambda-Lambda-sharp residual primitive F only by N^(1/2+o(1));
- the EMBF seminorm is therefore first-strip equivalent after replacing B_theta by F, with error N^(5/2+o(1));
- Abel summation of the endogenous weight differentiates F and returns block sums of the true prime residual f=Lambda-Lambda-sharp;
- current almost-all short-interval theorems do not control a fixed balanced multiplicative grid because their exceptional sets are much larger than the grid;
- the EMBF outer absolute value is exactly dual uniformity over arbitrary outer sign/phases; dropping it is a real weakening;
- ordinary Friedlander-Iwaniec asymptotic-sieve output applied separately to the two positive PESC lifts cannot certify cancellation of the common N^(3-o(1)) background;
- PACPSA difference stability is the only surviving parity-side mechanism;
- Campaign 32 attacks the asymptotic-sieve proof at the difference level.

No proof or disproof of RH is claimed.