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 three things simultaneously: intrinsic quantum geometry (U1), one fundamental matter-geometry dynamics (U2), and physical coreference of the quantum and classical descriptions through transformation (U3). We construct such a realization on an LP-typed causal-set history carrier. Its fundamental object is an exact all-stage, normalized, strongly positive projective decoherence functional D∞ together with a joint matter-geometry source functional Z∞[Jg,Jm]. Quantum matter and quantum geometry are observables of this same history dynamics rather than separately postulated sectors. La Profilée supplies the identity-under-transformation structure needed for U3. Q1 determines admissible continuation, Q2a the persistence class, Q2b continuation-stable history/profile identity, and π_p the bridge between microscopic histories and the identity-level description. We prove exact dynamical descent through this identity structure and all-stage existence of the microscopic H1-H3 construction. The resulting projective history representation yields Hilbert-space quantum mechanics, Born weights on decoherent records, and unitary evolution on the stated closed-identity sector. 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. On the certified Lorentzian continuum sector, the same fundamental dynamics admits controlled recovery descriptions. The BDG gravitational sector recovers Einstein-Hilbert gravity; covariant matter recovers renormalized QFT at each fixed perturbative order; the renormalized stress-energy tensor and a local nondegenerate solution branch close semiclassical backreaction. Geometric source deformations of the same decoherence functional generate quantum-geometric propagators, connected correlators, and 1PI response vertices. Hence QFT, quantum geometry, and GR arise as representations or controlled recoveries of one LP-identified physical dynamics, establishing U1 ∧ U2 ∧ U3. The exact fundamental theory is all-stage; the continuum QFT and GR statements have the explicitly proved recovery scopes stated below. The construction also yields further consequences without making them premises of unification. Sourcewise operator completeness gives an exact record-resolved isometry and therefore preserves encoded quantum information in the complete fine-history operator realization. In relativistic stellar collapse, regular continuation of the material persister beyond the first specified horizon/trapping event implies a horizon-constitution separation, with the Oppenheimer-Snyder solution providing an exact analytic witness. Selection Physics treats residual admissible microscopic non-uniqueness as an inference problem: nearby members are quantitatively distinguishable, a nonvanishing Einstein-Hilbert response is constructed, and a synthetic Source603 reconstruction demonstrates the transition from failed hard identification to nontrivial Bayesian information retention. Scope boundary. The fundamental LP history theory and its bounded cylinder source algebra are exact and nonperturbatively defined; the continuum QFT statements are controlled fixed-order recovery results. The paper does not require raw unit-weight quantum-measure concentration on the complete four-dimensional manifoldlike sector, nor a full unbounded nonperturbative interacting-continuum-QFT operator algebra. Those are stronger downstream questions. Likewise, the mathematical proper-time/Selection readout is constructed, while calibration of a real physical pre-target reconstruction kernel and an actual laboratory data channel remains empirical. Scope boundary. Two stronger questions are intentionally kept outside the premises of the unification theorem: raw qu