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. 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 quantum-measure concentration on the complete four-dimensional manifoldlike recovery sector, and equivalence with a full unbounded nonperturbative interacting-continuum-QFT operator algebra. The physical calibration of the real pre-target reconstruction kernel K_pre is likewise empirical. When reading an OPEN statement later in the paper, it should therefore be checked against this boundary before interpreting it as an open premise of the unification theorem. Universal closure and Selection Physics. Sections 31-32 strengthen the finite construction to the universal cylinder theory and prove the all-N H1-H3 microscopic existence theorem. The remaining admissible microscopic non-uniqueness is then treated as a separate physical question: which member is realized by nature? The Selection-Physics subsections establish quantitative distinguishability, information-retention criteria, intrinsic geometric carriers, gravitational response, member estimation, proper-time readout, and a synthetic blind-reconstruction/Bayesian bridge. These results do not reopen U1-U3. Exact theory versus recovery. The fundamental object is the all-stage projective history theory D∞ and its bounded joint source algebra Z∞[Jg,Jm]. C5 does not define or filter that dynamics; it identifies the sector on which comparison with continuum QFT and GR is controlled. Consequently, fixed-order renormalized QFT, Einstein-Hilbert recovery, stress-energy, and semiclassical backreaction are recovery theorems of the exact history theory rather than ingredients used to define it. Proof path. Sections 2-5 construct the LP-typed physical carrier and prove that the microscopic quantum dynamics descends through the identity structure. Sections 6-12 establish the controlled continuum interface, place matter and geometry in one history functional, recover the QFT and GR projections, and prove dynamical coreference. Sections 13-18 then show that quantum geometry is already an observable sector of the same decoherence functional and develop its continuum response hierarchy. Sections 21-28 collect these ingredients into the main theorem and its complete proof dossier. The paper is easiest to read as a proof of three obligations rather than as a catalogue of results. U1 asks whether geometry is intrinsically quantum in the fundamental theory. U2 asks whether matter and geometry belong to one dynamics. U3 asks whether the quantum-matter, quantum-geometric, and classical-spacetime descriptions demonstrably refer to the same physical subject through transformation. The main theorem closes the conjunction U1 ∧ U2 ∧ U3; the later consequences and Selection-Physics results are downstream of that closure.