# CSM_RH Paper 45 package

This package advances CSM_RH from state v1.35 to v1.36 inside Campaign 43.

Main certified results:

- exact factorisation-space Ramaré marking that preserves the restricted squarefree weight `r_X`;
- the large common-prime branch `p | (m,h)` is `O(X^(-31w/100+o(1)))`;
- the repeated-large-prime branch `p^2 | m` is also `O(X^(-31w/100+o(1)))`;
- the hard extracted branch reduces exactly to an affine prime-Liouville correlation with marked structured weights;
- double prime extraction gives only logarithmic incidence geometry at exponent resolution;
- polynomial-size extracted primes have only bounded prime-harmonic mass;
- the no-large-prime branch contains `X/(log X)^C` legal factorisation mass and a sign-coherent smooth subfamily.

WL2 closes as `CLOSED_AS_EXACT_MARKED_EXTRACTION_WITH_PRIME_HARMONIC_AND_SMOOTH_CARRIER_BARRIERS`.

Campaign 43 remains open.

Next continuation: Campaign 43 / WL3 — `STRUCTURED_WEIGHT_DECOUPLING`.

No RH proof or disproof is claimed.