# CSM_RH Paper 79 v0.1

Dyadic factor-scale localization of F-RH-024.

Main results:

- Define smooth prime-error block
  P_E(s)=sum Lambda(n)psi(n/E)n^-s - integral psi(x/E)x^-s dx.
- Smooth explicit formula:
  P_E(s)=-sum_rho E^(rho-s) psihat(rho-s)+trivial terms.
- At s=rho, the same zero contributes
  -m_rho psihat(0), exactly independent of factor scale E.
- Vaughan cofactor tail B_U(s)=zeta(s)M_U(s)-1 satisfies B_U(rho)=-1.
- Therefore every logarithmic e-scale carries the same +m_rho psihat(0) self-zero resonance.
- Rightmost-zero responses form an almost-periodic series in t=log E; long factor-scale averaging diagonalizes distinct ordinates and leaves positive self mass.
- The available factor-scale interval V<e<N/U has length (1-u-v)log N, so the universal pole is an accumulation of a growing number of equal-strength log-scale resonances.
- Corrects the naive edge-localization idea: the apparent E^(1-rho) growth was the unremoved prime main, not the zero resonance.
- Updates Paper78 literature scope: Bharadwaj-Rodgers 2026 reaches polynomial large-prime-factor correlations for well-distributed sequences, with support condition y_1+...+y_k<sigma; shifted primes have sigma=1/2.
- Complete complementary factorization e~N^theta, k~N^(1-theta) has total normalized log size 1, outside any sigma<1 support theorem.
- The shift-averaged sequence of Paper75 has deterministic level sigma<1-tau, still below 1.
- Opens F-RH-025: distributed Vaughan factor-scale defect power.
- No single theta block is the unique hard block; the root resonance is distributed across the full logarithmic factor strip.

No RH proof is claimed.