The Physical Unification of Quantum Mechanics and General Relativity - Quantum Matter, Quantum Gravity, and Dynamical Spacetime as Sectors of One Fundamental Physical Dynamics

Physical unification of quantum mechanics and general relativity requires intrinsic quantum geometry, one matter-geometry dynamics, and a criterion showing that the quantum and classical descriptions refer to the same physical subject through transformation. This paper constructs that architecture on an LP-typed causal-set history carrier. For each fixed admissible projectively consistent microscopic member, the fundamental object is a normalized strongly positive all-stage decoherence functional D∞ with a joint bounded matter-geometry source functional Z∞[Jg,Jm]. Quantum matter and quantum geometry are observables of that same history dynamics. La Profilée supplies the identity-under-transformation structure required for physical coreference. Q1 determines admissible continuation, Q2a the persistence class, Q2b continuation-stable history and profile identity, and πp the bridge between microscopic histories and the identity-level description. Exact descent and projective consistency establish a common quantum-history construction for every fixed admissible member. They do not select the numerical transition law that nature realizes. Figure 2. Intrinsic quantum geometry from the LP-CST decoherence functional. No external metric quantization is introduced: geometric correlators and 1PI response vertices are generated from the same history dynamics. The continuum QFT and Einstein statements are controlled recovery theorems in the declared LP scope. The fundamental law is the exact projective, strongly positive history family; interacting local QFT is its recovery description, not a second microscopic transition law. Theorems 210.1-214.1 close the previously isolated bridge by an exact projective source pullback and Tail-C5 recovery for all 32 generator incidences and all 80 induced neutrino strata. This edition also closes one independent finite physical gate: on the verified Shadow-MLS carrier, the free Dirac sector is realized in the exact Foldy-Wouthuysen representation through the conforming energy-square form. The finite recovery programme supplies a concrete common carrier. Three nested-history members pass global finite Shadow-MLS geometry tests. On the verified n233 member, 5,081 trial functions are globally well defined and reproduce constants. The earlier direct first-order compression produced a 20,324-dimensional spinor matrix and, after exact block reduction, a 10,162-dimensional generalized eigenproblem with at least 24 nonconstant low numerical modes. That calculation remains a valid diagnosis of the compressed candidate, not the physical no-doubling result of this edition. The replacement is analytic rather than fitted. Let L_N be the exact conforming Galerkin Laplacian on the same Shadow-MLS space and define H_N^FW = beta sqrt(m^2 + L_N). For m=1 on the unit three-torus, constants give exactly two positive spin modes at E=1. Every state orthogonal to them has zero mean and the torus Poincare inequality gives E >= sqrt(1+4 pi^2) > 6. Hence rank 1_(0,2)(H_N^FW)=2 exactly. The result holds at every admissible finite stage containing constants; it requires no spectral quadrature, no Wilson term, and no parameter chosen after viewing the n233 spectrum. The resulting claim is precise. LP fixes the identity-typed carrier and the conditions for common physical reference. A fixed admissible microscopic member fixes one exact projective matter-geometry theory. The bounded, gauge-invariant Domain observables of the four interacting matter families possess an exact projective and strongly positive common History-source lift, and the Tail-C5 theorems recover their fixed-order QFT correlators, stress-energy, Einstein regime, and nearby backreaction branch on that same carrier. All 32 generator incidences and all 80 induced neutrino strata inherit this lift. The verified carrier additionally supports an exact pollution-free free-Dirac realization. A particular P.428 cell-local discretization, an order-intrinsic Hadamard parametrix, a fully nonperturbative QFT sum, and empirical selection of the realized member are stronger tasks outside this theorem, not missing steps inside it. Sections 31 and 32 establish the projective cylinder theory, all-stage existence results, and microscopic non-uniqueness. Their recovery layer is completed by the exact source pullback and Tail-C5 result summarized in Section 33.5. Section 33 also separates the failed first-order compression from the new exact free-Dirac realization and proves the low-energy mode-count theorem. The paper therefore delivers the common dynamics, the interacting fixed-order recovery bridge, and a positive finite fermionic realization while retaining a strict boundary around stronger microscopic and nonperturbative claims.