A Conservative Analytical Framework for Macroscopic Fifth-Force Extraction: Trace Conservation, Positive-Definite Subspaces, and Epistemic Bounds

Title: A Conservative Analytical Framework for Macroscopic Fifth-Force Extraction: Trace Conservation, Positive-Definite Subspaces, and Epistemic Bounds Version 64. 2. 0 Update (The APS Prism Synthesis): This publication establishes theoretical claim discipline by structurally weaving immutable continuous physics together with stochastically-bounded operational subspaces. Formatted using equation-splitting and table configurations, it establishes a pristine experimental isolation chamber for the MICROSCOPE mission and future satellite tests of gravity: Protocol-Level Certification Bounds: Elevates the explicitly derived 10% drift scenario bound (₁₈₀ₒ 0. 131 meV) into the core analytical constraint of the framework. Generating a conservative lower-bound of SNR ₅₋₎₎ₑ = 2. 48, it triggers a statistically rigorous mandatory veto, acting as an absolute filter that prevents irreversible microstructural degradation and geometric Fisher deformation from being falsely published as a Type-I false positive. Dimensionally-Closed Thermodynamic Annealing: Replaces static temperature assumptions with a dynamic effective recovery threshold. The Wigner defect annealing recovery rate is formally parameterized to include a transient thermal spike tolerance (T ₌₈₂ₑ₎) that scales inversely with the hardware's degrading specific heat capacity, strictly preserving dimensional homogeneity (E/E=1) in the Arrhenius exponent. Moore-Penrose Pseudo-Inverse (D ₒ₍₀₏ₒ₇₎ₓ): Formally defines the unregularized pre-veto snapshot matrix via the pseudo-inverse (D ₒ₍₀₏ₒ₇₎ₓ (t) I (t) ^+) to guarantee global closure even on rank-deficient subspaces prior to Ridge normalization. Causally-Retarded Topological Telemetry: Eradicates discrete Boolean discontinuities and a-causal feedback loops. The Epoch-Commit protocol is mathematically governed by an infinitely differentiable logistic clearance function (S ₂₋₄₀ₑ) evaluating historical spectral power. This guarantees forward-time causality while preserving Jacobian smoothness. Files Included: main. pdf / main. tex: The definitive UNIFIED PRD manuscript. Prism/APS formatting integrated, multi-line equations split, tone neutralized, and mathematical custody established end-to-end. chameleonₗambertₘapper. py: Open-source Python toolkit (v64. 2. 0) simulating the logistic Epoch-Commit logic, dynamic Wigner annealing envelopes, trace conservation, and generating the Hardware Compliance Flowchart.