# CSM_RH Paper 52 v0.1

Campaign 44 / PK5-Z3 closure candidate.

Main results:

- Z3A: unit-ordinate zero clusters cost only O(log T).
- Z3B: separated Cauchy-type response windows have Schur Gram cost O(log^3 T).
- Refined low-frequency derivative localization removes a hidden coherent rank-one concern.
- Full zero-ensemble energy reduces to
  `O(log^3 T) * D_N(T)`,
  where
  `D_N(T)=sum N^(2 beta-2)/(1+|gamma|)^2`.
- Exact weighted-beta layer-cake identity.
- Top ordinate shell is automatically fixed-power admissible.
- Classical zero-density estimates do not by themselves certify the endpoint because they allow finite exceptional off-critical zeros.
- Z3 closes; Z4 becomes active.

No RH proof is claimed.