# CSM_RH Paper 16 v0.1

Campaign 15 audits the direct all-shift prime-correlation target against current average prime-pair and variance technology.

Main results:

- small shifts below N^(8/33+epsilon) are already harmless for every first target kappa<1/2;
- Matomäki-Radziwill-Tao provide broad averaged Hardy-Littlewood coverage but only arbitrary log-power precision in the von Mangoldt case;
- the authors explicitly distinguish this from divisor-correlation cases where power savings are available;
- recent higher-uniformity work for von Mangoldt still operates at log-power precision in the relevant statements;
- average-HL precision therefore addresses shift coverage, not the missing fixed-power exponent;
- BDH/AP variance weights differences by divisor kernels;
- Möbius inversion proves that the exact constant shift kernel is uniquely the q=1 mode;
- Selberg-integral and standard prime-pair variance routes are useful positive/quadratic tools but no lower-strength fixed-power bridge to PESC is identified;
- no audited shell produces a lower-strength fixed-power frontier;
- PESC remains the canonical target;
- Campaign 16 changes mode from representation generation to direct theorem generation.

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