Reduction of the Identity Orbital Integral to the Completed Spectral Zeta

Research Note 47 in the "Geometry of the Critical Line" programme. The prime-side kernel of the Weil explicit formula has been assembled from the SCT critical sector (Paper 47). This note reduces the remaining piece — the identity orbital integral I_id(h) — to a single decisive identification: the completed SCT spectral zeta must equal the completed Riemann zeta ξ(s) (up to normalisation). If this identification holds, the identity contribution matches the Weil archimedean distribution automatically via classical analytic number theory (Hadamard product, functional equation), the RTTC is a theorem, and the Riemann Hypothesis follows from self-adjointness of the critical operator. The note does not compute I_id…