Unified Information–Geometry–Dynamics Physics (UIGDP): A Deductive Framework Unifying Entanglement–Spacetime Reconstruction, Non-Adiabatic Thermodynamic Gauge Dynamics, and Quantum Measurement Projection within the ZFC Axiomatic Bridge

A central challenge at the frontier of theoretical physics is transforming qualitative analogies connecting quantum information, spacetime geometry, non-equilibrium thermodynamics, and quantum measurement into exact, falsifiable dynamical equations with proven domains of validity. In this paper, we establish Unified Information–Geometry–Dynamics Physics (UIGDP), a deductive physical framework anchored in our 71-page ZFC Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1] and synthesized with the Extended Quantum Information Geometry System (EQIGS, DOI: 10.5281/zenodo.23557698) [6], the High-Dimensional Geometric Probability System (HDGPS, DOI: 10.5281/zenodo.23557360) [4], and the Dynamic Topological Critical Transition System (DTCTS, DOI: 10.5281/zenodo.23557507) [5]. Condensing local Type III₁ quantum field algebras onto the Takesaki Type II₁ ground factor (ℳ_ground, τ_ground) governed by the universal quadruple 𝔘 = (𝒯_0x8A2C, 𝐂_UPTC, η_friction, ϵ_SHID), we formulate six core axioms (UIGDP-1 through UIGDP-6) and prove six fundamental theorems: (1) Necessary and Sufficient Curvature–Entanglement Conditions for reconstructing spacetime metric tensors g_μν^spacetime from Petz quantum Fisher information Hessians; (2) The Exact Unified IGD Master Cost Identity and Optimal Finite-Time Control Horizon τ⋆ = √((d_g² + Δ_ctrl²)/(2η_friction)); (3) Emergent Einstein–Cartan–Information Field Equations from modular entanglement equilibrium and Area-to-Volume phase transitions at D_crit = e^(𝐂_UPTC); (4) Dynamical Resolution of Quantum Measurement Projection via the URRHC Idempotent Monad 𝕄_URRHC (T² = T) with a testable dephasing floor; (5) Universal State Classification for Far-from-Equilibrium and Active Matter via Thermodynamic Length and Topological Persistence Dissipation; and (6) Quantum Simulator Advantage Thresholds under noise and control deficits. Complete Python numerical verification is provided in Appendix A.