# CSM_RH Paper 56 v0.1

Campaign 46 seeded shrinking-threshold package.

Main results:

- Seed PESC(kappa) gives pointwise `|psi(x)-x| << x^(1-kappa/2+o(1))`.
- This strengthens the bad-set estimate in the shrinking-threshold bridge.
- If
  `# {x: |U_H(x)| > H N^(-nu)} << N^(1-c)`
  at `H=N^alpha`, then
  `S_Lambda << N H^2 N^(-2nu) + N^(3-kappa-c+o(1))`.
- Effective lag exponent:
  `delta_ST=min(2nu, kappa+c+2alpha-2)`.
- Seeded PESC output:
  `kappa' < min(alpha,2nu,kappa+c+2alpha-2,2-alpha(2-kappa))`.
- Strict gate:
  `alpha>kappa`, `nu>kappa/2`, `c>2(1-alpha)`.
- For modest c, optimal scale:
  `alpha*=1-c/(4-kappa)`,
  output
  `kappa+c(2-kappa)/(4-kappa)`,
  unless threshold precision bottlenecks.
- Seed relocates the old Paper-38 right edge from sigma->1 to sigma=1-kappa/2.
- Standard finite moment + Markov zero-packet methods cannot cross threshold `nu=kappa/2` while the boundary packet remains admissible.
- New direct frontier F-RH-017: seeded supercritical shrinking-threshold exceptional set.
- SG3 zero-detector/coercivity route is next.

No RH proof is claimed.