# CSM_RH Paper 77 v0.1

C47-B-v2 completed.

Main results:

- Applies exact Vaughan identity directly to the signed root sequence f_{N,H}.
- Adds log-weighted divisor law:
  G_d=G/d+O(N), with aggregate ND polylog discrepancy.
- Exact Type-I recombination:
  M_{U,V}=F[M_U(log N-L_V)-J_U-1]+G M_U.
- Exact root identity:
  R_W=M_{U,V}-TII_{U,V}+E_I
     =-(TII_{U,V}-M_{U,V})+E_I.
- Type-I error:
  E_I << N U V log^O(1) N.
- For H=N^(1-tau), U=N^u, V=N^v:
  Type-I saving exponent = 1-tau-u-v.
- Therefore Type I is supercritical whenever
  u+v<1-tau-kappa-eta.
- Under PESC, explicit main M_{U,V} has scale roughly
  NH N^(-d) U^(-d), d=kappa/2,
  which is generally larger than root-critical N^-kappa for u<1.
- Thus the Type-II term itself must contain a matching one-point truncation counterterm.
- The correct target is NOT TII smallness.
- Opens F-RH-024:
  |TII_{U,V}-M_{U,V}| << NH N^(-kappa-eta).
- Combined with the deterministic Type-I error, F-RH-024 gives direct root covariance excess with no generic sieve log floor.
- F-RH-023 is downgraded to auxiliary parity candidate; F-RH-024 is preferred root arithmetic input.

No RH proof is claimed.