# CSM_RH Paper 67 v0.1

PT6F low-conductor character annihilation audit.

Main results:

- Signed complete-period cancellation:
  sum_{h<=H} chi(h+r)=O(q) for nonprincipal chi mod q.
- But for every p>0:
  sum_{h<=H}|chi(h+r)|^p = (phi(q)/q)H + O(q).
  Thus fixed low-q character harmonics survive every absolute shift Lp norm.
- L1 duality makes the obstruction exact: dual signs can align with conjugate character values and reverse periodic cancellation into a coherent sum.
- For a fixed prime modulus ell and nonprincipal chi:
  sum_{a in F_ell^*} chi(a+h) = -chi(h) for h nonzero mod ell.
- Hence even perfectly equidistributed ordinary primes have a shifted-character local profile
  -chi(h) Li(X)/(ell-1).
- Low-q nonprincipal modes can therefore include legitimate local arithmetic factors, not merely bad spectral pollution.
- Simple PT6F annihilation is closed as nonviable for absolute/ex\-ceptional norms.
- New track PT6G: low-conductor local-factor renormalized dispersion.

No RH proof is claimed.