# CSM_RH Paper 64 v0.1

PT6 low-frequency structural audit.

Main results:

- Selberg symmetry error form:
  R(x) log x + sum Lambda(n) R(x/n) = O(x).
- A boundary power mode R_rho(y)=y^rho is mapped by the Selberg convolution to x/(1-rho)+lower order, exactly the O(x) scale already allowed. Standard Selberg symmetry therefore does not contract a fixed power exponent.
- Constructs an integer-lattice pseudo-prime set P* with weights 0/log n such that:
  Theta*(x)=x+eps x^(1-d) cos(gamma log x)+O(log x),
  pi*(x)~x/log x.
- Thus positivity, integer support, log-sized jumps, monotonicity, and prime-like sparsity are all compatible with a persistent boundary harmonic.
- Broucke 2026 Beurling constructions give a complementary model: positive Euler-product generalized primes can have prescribed zero contours and near-sharp PNT errors.
- Together the models isolate the remaining structure as the simultaneous ordinary additive lattice + exact integer factorization.
- Audits arithmetic-progression replication: principal zeta error can be copied across moduli, but classical BDH has an x^2/log^A x remainder which masks every fixed x^(2-2d) boundary contribution.
- PT6E opens: ordinary-integer factorization/additive-lattice low-frequency excess.

No RH proof is claimed.