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 (GHCP(t)) dynamically deforms in response to the fast-time analog slew rate, organically widening the variance envelope along the HCP slip planes (PHCP) 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⁾ / cₚᵉᶠᶠ(τₙ)), 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 (Sθ̂) is updated via a strict discrete protocol. The frozen operational reference point (θ̃ref) 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. chameleon_lambert_mapper.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.