# CSM_RH Paper 23 v0.1

Campaign 22 proves an exact dyadic Haar resolution of jump energy and shows why it does not by itself force polynomial-scale decorrelation.

Main results:
- exact identity sum_j D(2^j)/4^(j+1) = sum_n |a_n|^2 for every finite sequence;
- for a_n=Lambda(n)-1 the total weighted octave energy is asymptotic to X log X;
- total octave energy can be localized at microscopic scales;
- a high-frequency oscillatory component can carry X log X jump energy while a smooth drift dominates polynomial lag energies and remains critically locked;
- diagonal injection and generic Littlewood-Paley theory therefore do not prove PDSD;
- PDSD remains a valid but optional strong sufficient mechanism;
- the direct MLEPG/PESC path remains shortest;
- Campaign 23 returns to prime-side fixed-power candidate generation with prime-specific low-frequency arithmetic required.

No proof or disproof of RH is claimed.