# CSM_RH Paper 50 v0.1

Campaign 44 / PK4 closure candidate.

Main outputs:

- exact prime-only / von Mangoldt centered transform split;
- pointwise prime-power correction `O(N^{-1/2} min(|t|,1))`;
- middle-band prime-power energy `O(N^{-1})`;
- explicit cross-term control in the weighted Hilbert norm;
- exact discrete Abel identity
  `L_N(t)=sum_{m=N}^{2N-1}(psi(m)-m)(g(m)-g(m+1))`;
- PK4 closure candidate and PK5 zero-response task sequence.

No PESC fixed-power theorem and no RH theorem are claimed.