# CSM_RH Paper 19 v0.1

Campaign 18 audits the principal Fejer arc against current large-value, zero-density, and exceptional-set technology.

Main results:

- Guth-Maynard already prove an explicit-formula L2 zero-packet estimate at the short-interval scale with subpower exponential saving.
- Abstract zero-density law:
  c_A(alpha)=2-A(1-alpha).
- The range threshold is alpha>1-2/A; for A=30/13 this is alpha>2/15.
- If the zero-free gap eta(T) shrinks to zero, the strongest fixed-exponent gain from the absolute density schema is c_A(alpha) eta(T)=o(1).
- Even the ideal density exponent A=2 would improve range but not create a fixed power while eta(T)->0.
- Gafni-Tao exceptional-set machinery uses fixed relative-error tolerances; it does not provide a polynomially shrinking good-interval threshold.
- Density information is blind to a finite number of persistent off-axis zeros.
- The direct PESC/MLEPG branch therefore closes back to the earlier fixed-zero-strip strength core.
- Campaign 19 requires a single-zero-sensitive mechanism rather than another density improvement.

No proof or disproof of RH is claimed.
No live GLM provider run is claimed.