# CSM_RH Paper 31 v0.1

Campaign 30 connects the classical sieve parity problem directly to the already-audited PESC parity branch.

Main results:
- exact positivity-lift identity: prime-detection difference equals 2 PESC;
- replacing prime detection by von Mangoldt detection changes the first-strip target only by prime-power error O(N^(5/2+o(1)));
- Friedlander-Iwaniec's parity-breaking bilinear axiom is Möbius-sensitive and distinguishes Liouville parity twins;
- when applied to the two PESC positivity lifts, the difference seminorm is exactly the EMBF geometry from Paper 13;
- therefore classical parity breaking is already present in the CSM_RH EMBF/PACPSA branch;
- PESC needs both parity cancellation and endogenous fidelity to the cumulative prime-error weight;
- a direct rough-Liouville fixed-power scalar is inverse-zeta locked and already fixed-strip strength;
- classical asymptotic-sieve output has log-relative rather than fixed-power precision;
- no new parity frontier is created;
- Campaign 31 reaudits EMBF using the later Lambda-sharp/residual and modern higher-uniformity insights.

No proof or disproof of RH is claimed.