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 Iᵢd (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 Iᵢd from first principles; it reduces the computation to the completed spectral zeta identification. Four pieces of evidence are assembled (pole structure, prime coefficients, archimedean Γ-factor, functional equation) and explicitly labelled as motivation, not proof.