# CSM_RH Paper 76 v0.1

Campaign 47 correction and extraction audit.

Key results:

- Define signed root sequence:
  Q_H(n)=sum_r omega_H(r)(Lambda(n+r)-1),
  f_{N,H}(n)=W(n/N)Q_H(n).
- Exact root identity:
  R_W=sum_n (Lambda(n)-1)f(n)=sum_n Lambda(n)f(n)-F.
- Nonnegative Paper75 sequence satisfies a=H W+f.
- Exact correction:
  P-A = H(L_W-M_W)+R_W.
- Therefore P=A+power does NOT directly give root pair residual.
  It leaves the one-point term H(L_W-M_W), controlled by PESC only at exponent d=kappa/2.
- Opens correction C-RH-005.
- Signed sequence still has deterministic divisor law:
  F_d=F/d+O_W(N).
- Thus strong aggregate local distribution survives.
- Vaughan/Heath-Brown exact identities can preserve fixed-power Type I/II errors; Ford-Maynard records Vaughan sufficiency gamma+nu>1 and gives a general asymptotic criterion.
- But Paper75 F-RH-023 is not Vaughan's balanced Type-II form:
  F-RH-023 uses gamma(n,C)mu(mn);
  Vaughan uses Lambda(m)b_V(k).
- Generic comparison-sequence Vaughan Type I includes m=1 and is limited by the one-point seed exponent d.
- Campaign47 extraction fork:
  aggregate FI sieve uses strong divisor law but has log extraction floor;
  exact identities preserve power but require different balanced input and generic Type-I is seed-limited.
- F-RH-023 remains an open parity input candidate, but its root sufficiency is not certified.
- Next: C47-B-v2 exact Vaughan decomposition directly on signed f, keeping F_d=F/d main terms exactly.

No RH proof is claimed.