# CSM_RH Paper 57 v0.1

Campaign 46 / SG3 detector audit.

Main results:

- Defines the classical Turan-Gallagher detector energy D_w(x).
- Seed PESC(kappa) gives:
  D_w(x) << x^(-kappa+2/B+o(1)) for x>=T^B.
- Classical Turan detector lower bound from a zero at radius r:
  D_w(x) >> x^(-C r) log^3 x.
- Hence this detector can improve the seed only if C<2.
  Published classical constants are far larger, so the standard route is non-amplifying.
- Defines secondary frontier F-RH-018:
  a detector upper exponent lambda > C kappa/2.
- Seed-shifted Mellin derivative bounds grow like m! r^(-m-1).
- A boundary pole has exactly the same derivative growth.
- Critical log-time normalization turns a boundary zero into a persistent harmonic.
- Concludes that seed PESC alone supplies no single-zero coercivity margin.
- SG3 standard detector route closes; SG4 becomes active.

No RH proof is claimed.