# CSM_RH Paper 68 v0.1

Key results:

- Exact local shifted-prime Möbius factor:
  kappa_l(h)=1 if l|h;
  otherwise (l^2-3l+1)/(l(l-1)).
- Finite low-q profiles recombine exactly by CRT into an Euler product.
- Fixed-shift and shift-averaged products have sieve dimension two:
  ~ constant/(log z)^2.
- Therefore local-factor renormalization is intrinsically logarithmic, not fixed-power.
- PESC seed d=kappa/2 gives fixed-power cancellation in the signed shifted-prime average when H=X^(1-tau), tau<d.
- The unresolved gap is signed-to-absolute.
- A sufficient L2 target is the prime-pair averaged two-point Chowla energy.
- F-RH-020 is opened as AUXILIARY ONLY; no root bridge to F-RH-017-v3 is claimed.

No RH proof is claimed.