A Conservative Analytical Framework for Macroscopic Fifth-Force Extraction: Dynamic Thermal Bounds and TA6V Empirical Closure

Title: A Conservative Analytical Framework for Macroscopic Fifth-Force Extraction: Dynamic Thermal Bounds and TA6V Empirical ClosureVersion v18 (The Objective Closure Synthesis): This publication establishes theoretical claim discipline by structurally weaving continuous physics together with stochastically-bounded operational subspaces. Formatted using advanced equation-splitting, float-fixing, and double-column table configurations, it establishes a conservatively bounded operational limit and serves as a foundational mathematical engine for an upcoming advanced audit protocol. Empirical TA6V Hardware Limits Front-Loaded: Resolves the empirical material gap by concurrently evaluating the TA6V Titanium alloy parameters (420 K Debye temperature) utilized in actual space accelerometers alongside the theoretical high-stiffness Beryllium proxy. The 2. 491 SNR veto threshold is established as the primary structural boundary in the abstract. Chronological Navigational Motifs: Grounds the theoretical derivations using explicit textual markers ("Step X of the Exact-Closure Map"). The manuscript traces a singular data point from theoretical vacuum through the physical proxy lattice and into the discrete Analog-to-Digital Converter quantization limits, preventing cognitive disconnect during phase transitions. Physical Grounding of the Environmental Tensor: Abstracts the physical degradation vector into a generalized modular tensor (Dn), while physically justifying the 40 percent specific heat capacity degradation by detailing the specific elastoplastic response and kinetic energy-trapping mechanisms of the TA6V lattice compared to rigid proxies. Pristine Vacuum True-Positive Verification: Proves the diagnostic acts as a targeted filter rather than a blind wall. The framework explicitly contrasts a 2. 51 SNR true cosmological signal (domain wall) against the 2. 491 SNR hardware drift, demonstrating that the causally-retarded logistic gate preserves sustained topological features while quarantining transient thermal artifacts. Theoretical Modularity Appendix: To preserve the structural impact of the primary empirical validation, the canonical Symmetron tensor contraction proof is subordinated to Appendix A, demonstrating formal modularity without interrupting the primary scientific product. Files Included: mainᵥ7700. pdf / mainᵥ7700. tex: The definitive manuscript. PRD formatting integrated, rhetorical muting applied, TA6V limits front-loaded, chronological motifs embedded, and Symmetron proofs moved to the Appendix. chameleonₗambertₘapperᵥ77. py: Open-source Python toolkit (v77. 0. 0) simulating concurrent TA6V bounds, true-positive vs false-positive vacuum diagnostics, and generating the Hardware Compliance Flowchart.