# CSM_RH Paper 74 v0.1

Campaign 46 structural closure.

Main results:

- Uses Chou-Haag-Huryn-Ledoan 2026 ordinary prime-pair error theorem:
  E_pp(N)=Omega(N^(1+2Theta-eps)), Theta=sup Re zeta zeros.
- Therefore any upper E_pp(N)<<N^(3-s+o(1)) forces Theta<=1-s/2.
- If a PESC(kappa) seed is saturated by Theta=1-kappa/2, then
  E_pp(N)=Omega(N^(3-kappa-eps));
  any fixed saving beyond kappa is root-level progress.
- Their conjectural E_pp~N^2 log^2 N implies RH.
- Even GRH for Dirichlet L-functions gives only N^(5/2) polylog upper in their theorem, illustrating that prime-pair error contains additional arithmetic difficulty.
- Audits Selberg/GPY/Maynard positivity: no signed fixed-power q=1 residual.
- Audits dispersion: true power savings exist for prime x divisor-like problems and high-dimensional modulus averages, not automatically for prime x prime q=1.
- Parry 2026 provides a contemporary example of power-saving sign cancellation in large modulus-family averages, reinforcing the distinction.
- Combined with Paper 73's exact central-energy/zero-strip equivalence, PAIR5D is now identified as genuine RH-level arithmetic input, not a free structural amplifier.
- Campaign 46 status:
  CLOSED_AT_RH_EQUIVALENT_ARITHMETIC_WALL.
- Root frontiers F-RH-017-v3, F-RH-022, PAIR5D remain open.
- Suggested next phase: Campaign 47 ORDINARY_PRIME_BOUNDARY_BREAKING, only if a new explicit q=1 fixed-power arithmetic inequality is proposed.

No RH proof is claimed.