# CSM_RH Paper 33 v0.1

Campaign 32 audits PACPSA as a true difference-level sieve problem.

Main results:
- exact identities can cancel the common positive background of the two PESC lifts;
- modern Ford-Maynard Type-I/II sieve theory confirms that signed difference-level prime detection is feasible at arbitrary log-power accuracy;
- in the classical Friedlander-Iwaniec proof, Section 6 contains a main-density leakage A(x) log(delta)/log(Delta);
- after coupled linearization the common background cancels, but the signed perturbation total H_h survives in this leakage;
- mean-zero recentering kills this zeroth mode in the signed perturbation but exports the same smooth drift into an exact rank-one scalar H_h G_N/W_N;
- on a power drift B(x)~x^beta this scalar has PESC scale N^(2 beta+1);
- signed Type-I and EMBF-like Type-II estimates are still required;
- PACPSA difference stability alone is therefore insufficient and is demoted to an auxiliary coupled-sieve program;
- Campaign 33 attacks the exposed low-frequency rank-one scalar directly.

No proof or disproof of RH is claimed.