# CSM_RH Paper 54 v0.1

Campaign 45 seeded amplification package.

Main results:

- Reuses an existing PESC(kappa) estimate inside the residue-chain anchor.
- Seeded bridge:
  `kappa' < min(alpha, delta, 2-alpha(2-kappa))`.
- Strict MLEPG amplification iff:
  `alpha > kappa` and `delta > kappa` with `alpha<1`.
- Optimal natural-scale map:
  `Phi(kappa)=2/(3-kappa)`.
- Exact iteration converges geometrically to 1.
- Conditional bootstrap meta-theorem: a fixed seed plus natural MLEPG at every seeded optimal scale would imply RH.
- Critical power-law sequence `u_n=n^(1-kappa/2)` proves PESC alone cannot deterministically generate `delta>kappa`.
- Dyadic contraction-mass version of the amplifier gate is certified.
- Seed gate and arithmetic amplifier gate remain open.

No RH proof is claimed.