Title: The Holographic Origin of Active Geometry: Endogenous Metric Deformation

This work presents a unified field equation on the principal bundle of oriented frames P = SO(M), resolving the dualism between macroscopic kinematics and microscopic structural reconfiguration. We treat the metric structure not as a fixed background, but as an endogenous degree of freedom capable of active reconfiguration. Key Innovations and Results: Holographic Metric Determination: Macroscopic geometry emerges as a holographic imprint of the microscopic algebra of constraints. Active degrees of freedom are dynamically filtered through an intersection of operator cones, generating the metric tensor G(X) from the local structural potential J_IR. Active Geometrodynamics: Metric curvature arises as an endogenous nonlinear deformation induced by the Hessian of the potential. This process transforms topological barriers into permeable corridors through a spectral reconfiguration of mobility. Metric Short-Circuiting (Theorem 2): Utilizing Yosida regularization, we demonstrate how frame orthogonality initiates the annihilation of the effective interval (ds²_eff → 0), topologically regularizing singularities. Phase Accumulation Law (Theorem 1): We derive the dynamics of reconfiguration from a variational balance principle of least geometric resistance. Empirical Validation: The model confirms the regime of Harmonic Resilience (γ ≈ 2), demonstrating that active systems can undergo reversible metric deformations where passive media would experience brittle failure. Keywords: Unified Field Equation, Active Geometrodynamics, Endogenous Metric Deformation, Holographic Metric Determination, Information–Metric Coupling, Micro–Macro Dynamics, Yosida Regularization, Convex Cone Intersection, Hessian Geometry, Critical Metric Corridor (CMC), Metric Short-Circuiting, Orthogonal Resonance, Topological Phase Transition, Harmonic Resilience.