# CSM_RH Paper 25 v0.1

Campaign 24 reduces the centered fourth-moment candidate to its fully distinct four-point sector.

Main results:
- exact partition of the quartic expansion by offset collisions;
- every collision sector is O(X H^3 log^4 X);
- for any eta in (0,1], a bound A4_dist << X H^(4-eta) polylog implies C4HEG;
- Gallagher/Klimov raw moment bounds are uncentered and cannot be algebraically centered using independent upper bounds;
- the unconditional raw fourth moment retains H^4 leading scale;
- 2026 short-interval higher uniformity is structurally strong but quantitatively log/subpower for Lambda;
- the first irreducible nonlinear core is the fully distinct three-dimensional centered four-point aggregate;
- Campaign 25 attacks this aggregate directly.

No proof or disproof of RH is claimed.