# CSM_RH Paper 24 v0.1

Campaign 23 generates a new nonlinear prime-side fixed-power candidate and closes a one-point shortcut.

Main results:
- explicit sparse nonnegative spike model with prime-like density, height, lower bound, total mass, and X log X jump energy, but with cumulative drift n^beta and polynomial-scale critical locking;
- one-point prime-like constraints therefore do not prevent smooth low-frequency drift;
- new candidate C4HEG: any fixed H-exponent improvement in the centered fourth short-interval moment creates a fixed X-power at polynomial H;
- C4HEG(alpha,eta) implies kappa < min(alpha eta / 2, 2-2 alpha);
- the conjectural Gaussian fourth moment is much stronger, corresponding roughly to eta=2;
- current raw Gallagher/Klimov sieve moment bounds retain H^4 scale at fourth order and do not give eta>0 after crude centering;
- Campaign 24 attacks the centered four-point correlation aggregate.

No proof or disproof of RH is claimed.