# CSM_RH Paper 63 v0.1

MRSTT proof-slack audit and stronger anchor barrier.

Main results:

- MRSTT Lemma 3.5's H2<=X/W^4 is not intrinsic; the underlying variance proof can use a target-dependent condition H2<=X/W^q with q>2+a/2.
- Baker-Harman-Pintz gives W^-1/3 up to logs, so any mean-square exponent a<1/3 is available from the same proof.
- Chebyshev can be asymmetric: threshold W^-b and exception W^-c0 are allowed whenever 2b+c0<a.
- Optimizing all current-proof slack gives:
  2 nu_diff + c_diff < (2/13) tau.
- This improves Paper 62's crude tau/40 symmetric ceiling but remains far below the amplifier gate.
- Stronger result: any scale-comparison plus a long interval controlled only by seed PESC has anchor threshold exponent at most d=kappa/2.
- Even perfect scale coherence cannot prove F-RH-017-v3, which requires nu>d.
- A hypothetical boundary zero saturates the anchor ceiling exactly: normalized interval averages preserve H X^-d amplitude across scales.
- Higher-order scale filters may improve low-frequency technical errors but cancel the same smooth boundary mode and must recover it through an anchor.
- Guth-Maynard large-value improvements affect the high-frequency residual but do not remove the critical long-anchor barrier.
- PT6 opens: direct low-Mellin-frequency boundary-packet suppression.

No RH proof is claimed.