The Structural Unification of Quantum Mechanics and General Relativity

La Profilée supplies the structural architecture of determination, Constitution, identity under transformation, and coexistence. It constrains admissible physical constructions without determining measured constants or selecting a unique microscopic member. This paper inserts the identity architectures established for quantum mechanics and general relativity into the quantum-gravity problem and constructs their common physical reference on a premetric history carrier. Constitution is prior to transformation. Role completeness of Frame, Module, and Coupling is distinguished from completeness of a physical profile. Completed compatible profiles are globally glued and quotiented by constitutional identity before residual multiplicity or actuality is assessed. Q1 determines the relevant bearer; Q2a its persistence class; Q2b its continuation-stable profile; and the persistence bridge connects history and state descriptions. These relations are not identified with the constitutional quotient. The fixed-background argument is made only under strict coreference of object, level, aspect, and transformation class. Quantum mechanics and general relativity alone do not entail a blanket logical contradiction. The constructive requirement is stronger and more useful: intrinsic quantum geometry, one matter–geometry dynamics, and physical coreference across their quantum and classical descriptions. For each fixed admissible projective microscopic member, the construction supplies a normalized strongly positive all-stage decoherence functional and a joint bounded matter–geometry source algebra. Theorem 32.19 of the current unification V4 collects this internal common-dynamics and recovery construction. The exact source pullback and Tail-C5 results close the controlled interacting fixed-order QFT/GR bridge over all 32 declared generator incidences and 80 induced neutrino strata, with nonempty recovery-admissible state fibres. The original two-level identity construction, causal-set examples, detector calculations, channel witnesses, and sample-wise recovery proofs remain part of the paper. Their scope is retained. In particular, an inserted verdict suppressor is a comparison construction, not an admissible modification of the fundamental dynamics. The older scalar phase candidate is not used to infer projectivity without the vector-sum condition. A separate exact free Dirac realization on the conforming Shadow-MLS carrier has precisely two positive modes below energy two on the unit torus at mass one. The completion is premise-relative: stronger local interacting discretizations, nonperturbative summation, and empirical selection are beyond the stated theorem.