# CSM_RH Paper 62 v0.1

Campaign 46 seeded MRSTT insertion.

Main results:

- Seed PESC(kappa), d=kappa/2, implies Mertens bound M(x)<<x^(1-d+o(1)).
- Hence dyadic mu and Lambda-1 Dirichlet polynomials obey fixed-power bounds:
  |D(1+it)| << (1+|t|) L^(-d+o(1)).
- In the MRSTT Heath-Brown Type-II decomposition, every side has at most five 1/log/mu blocks and support >=X^epsilon0, hence contains a block of scale >=X^(epsilon0/5).
- If tau+4w/3 < d epsilon0/5, the seed verifies MRSTT Lemma 3.5 with polynomial W=X^w rather than log^A X.
- This yields fixed-power scale coherence and a genuine seeded almost-all short-interval PNT power saving.
- Safe explicit example:
  tau=d epsilon0/100,
  w=tau/8,
  eta=d epsilon0/8000.
- However Lemma 3.5 requires H2<=X/W^4, hence w<=tau/4, and outputs only W^-1/10 saving.
- Therefore its threshold and exception exponents are at most tau/40, while F-RH-017-v3 requires nu>d and c>tau in the seed-compatible tau<<d regime.
- Thus current MRSTT Type-II geometry cannot amplify PESC even after seed upgrades the Dirichlet-polynomial input to fixed power.
- A polylog rough-number approximant is uniformly polynomially flat, but its residual retains every nontrivial zeta zero pole.
- The remaining problem is boundary-crossing Type-II large deviation, not log-to-power conversion.

No RH proof is claimed.