A Reality-Strict Analytical Framework for Macroscopic Fifth-Force Extraction: Non-Stationary Matérn Covariances, Covariant Thermodyamics, and Observable Subspaces

Version 52. 0. 0 Update (The Unified Phenomenological Synthesis): This publication establishes theoretical claim discipline by structurally aligning the mathematical framework so that physical mechanisms explicitly drive all statistical and operational bounds: Non-Stationary Matérn Defect Bridge: The spatial continuum-to-discrete map utilizes an explicitly defined Matérn covariance (K₃/₂). To account for transient structural plasticity during multi-shock events, the Mahalanobis distance metric (G ₇₂₏ (t) ) dynamically deforms in response to the fast-time analog slew rate, organically widening the variance envelope along the HCP slip planes (P ₇₂₏) before cleanly snapping back to baseline. Covariant Algebraic Floor: The thermal windowing trigger is insulated against specific heat depletion and cryogenic microphonic harmonic beating. The macroscopic Zero-Point Energy limit is dynamically scaled by the inverse of the specific heat ratio (cₚ^ (0) / cₚ^ eff (ₙ) ), creating a covariant algebraic floor that hardens seamlessly as the physical instrument fatigues. Occlusion-Bound Slow-Time Metric Updates: To prevent geometric paradoxes and 3rd-order Lambert-W₀ nonlinearities during 10% parameter drift scenarios, the Anisotropic Scaling Metric (S_) is updated via a strict discrete protocol. The frozen operational reference point (ₑ₄₅) is re-centered exclusively during the planetary occlusion Recalibration Reentry Protocol, clearing epistemic bias without corrupting live-telemetry Hessian bounds. Asymptotic Local Risk & Reproducible Drift Limits: Extraction confidence evaluates the Asymptotic Local Risk Model. A concrete numerical scenario is explicitly derived step-by-step: assuming a 10% parameter drift, the exact evaluated baseline variance (0. 9216 meV²) paired with an exact remainder-bounded physical target shift (0. 131 meV) mathematically forces the operational Signal-to-Noise Ratio to 2. 48, triggering a macroscopic extraction veto. The subsequent planetary occlusion successfully recenters the target shift to zero. Files Included: main. pdf / main. tex: The definitive UNIFIED PRD manuscript featuring objective claim discipline, explicit numerical evaluations, fully-closed causal diagrams, 8 embedded figures, and a complete bibliography. chameleonₗambertₘapper. py: Open-source Python toolkit (v52. 0. 0) simulating the Asymptotic Local Risk stabilization, Non-Stationary Matérn Deformations, Covariant Algebraic Floors, Parseval anti-aliasing cutoffs, and the physically mapped Eötvös target bias with occlusion-bound recentering.