# CSM_RH Paper 65 v0.1

PT6E twisted-factorization and character-family audit.

Main results:

- Exact ordinary factorization:
  Lambda = mu * log.
- At a zeta zero rho of multiplicity m:
  -zeta'/zeta = -m/(s-rho)+O(1).
  Thus Möbius cancellation does not self-improve the prime error; exact factorization preserves the boundary pole.
- Character-twisted exact identity:
  chi Lambda = (chi mu) * (chi log),
  with Dirichlet series -L'/L.
- Every Dirichlet L zero is therefore pole-preserved in the corresponding twisted prime channel.
- PESC seed lifts to principal characters because L(s,chi0)=zeta(s) times finite Euler factors.
- Lichtman's shifted-prime Möbius proof uses all characters modulo q on major arcs; its key prime-polynomial input explicitly uses zero-free regions for L(s,chi).
- Therefore a zeta seed cannot naively upgrade the major-arc parameter W from log-power to polynomial power: nonprincipal L-functions become a genuine family barrier.
- Principal-only power improvement cannot control the Fourier supremum.
- New frontier F-RH-019: averaged-character major-arc power without proving individual family strips.

No RH proof is claimed.