Residue Packaging for the Quotient Trace: RTTC-6 in Theorem-Safe Form

Research Note 45 in the "Geometry of the Critical Line" programme. RN44 established the structural form of Wall 3: the correct operation is a Connes-style distributional quotient trace over spatial scaling orbits, governed by the geometric carrier pole at s = 1. This note isolates the remaining analytic task: packaging the residue prescription in theorem-safe form. It defines the quotient-trace residue object directly in the Mellin domain, separates the identity singularity from the prime-power terms, and records four exact conditions under which the Wall 3 prescription is well-defined: geometric pole control, identity singularity isolation, prime-side holomorphy (absolute convergence with super-exponential…