# CSM_RH Paper 60 v0.1

Campaign 46 / F-RH-017-v2 sharpness package.

Main results:

- Applies Pintz's Mellin-pole mean-absolute theorem to normalized multiplicative short-interval differences.
- Mellin multiplier:
  Q_h(s)=((1+h)^s-1)/h -> s,
  with uniform analytic/growth bounds for 0<h<=h0.
- A fixed zeta zero rho=beta+i gamma forces:
  int_1^Y |A((1+h)x)-A(x)| dx >>_rho h Y^(beta+1).
- Under seed PESC(kappa), a boundary zero beta=1-kappa/2 and h=Y^-tau forces at least Y^(1-tau-o(1)) supercritical exceptional mass.
- Near-boundary zero beta=1-kappa/2-delta forces at least Y^(1-tau-delta-o(1)) exceptional mass when nu>kappa/2+delta.
- Deterministic one-jump-per-residue-chain model proves c>tau is sharp for the fixed-H L1 converter.
- Smooth boundary mode proves nu>kappa/2 is sharp.
- Therefore F-RH-017-v2 is parameter-sharp; no further deterministic bridge optimization remains.

No RH proof is claimed.