# CSM_RH Paper 17 v0.1

Campaign 16 is the first direct theorem-generation round after representation generation was stopped.

Main results:

- A deterministic residue-chain inequality converts one fixed additive lag-energy estimate into global PNT mean-square control.
- This yields the first direct new theorem candidate MLEPG.
- MLEPG(alpha,delta):
  S_Lambda(N,H) << N H polylog(N) + N H^2 N^(-delta+o(1))
  at H=N^(alpha+o(1)).
- For 0<alpha<2/3 and delta>0, MLEPG implies a fixed global mean-square power and therefore returns to PESC.
- The current Matomaki-Radziwill-Tao average Hardy-Littlewood theorem yields only the same structure with log^(-A) instead of N^(-delta).
- The missing power is localized to one signed triangular aggregate of prime-pair errors.
- Shiftwise power-saving Hardy-Littlewood is unnecessary and is rejected as too strong.
- Campaign 17 is prepared to attack the triangular signed error before absolute values are taken.

No proof or disproof of RH is claimed.
No live GLM provider run is claimed.