A Reality-Strict Analytical Framework for Macroscopic Fifth-Force Extraction: Sensitivity Derivatives, Trace Conservation, and Observable Subspaces

Version 61. 0. 0 Update (The Sensitivity-Calibrated Epistemic Closure): This final publication establishes theoretical claim discipline by structurally separating immutable physics from engineered hardware limits and mathematically justifying all operational setpoints: Linguistic & Epistemological Airlocks: Absolute deterministic verbs are strictly quarantined to continuous physical laws. Phenomenological limits use bounded language ("provides a bounded geometric constraint", "enforces the operational condition"). Topological Trace Conservation: Explicitly proves that the dimensionless Mahalanobis distance metric conserves its spatial trace (Tr (G ₇₂₏ (t) ) 3) during fast-time non-stationary Matérn deformation. Sub-Multiplicative Transduction Bounds: Establishes a strict sub-multiplicative upper limit on the linear transduction matrix to prove it mathematically subordinates the spatial variance envelope without bleeding into electrical RC latency boundaries. Bounded Sensitivity Derivatives: All tunable operational heuristics are mathematically justified against cryogenic fluctuations. Explicit lemmas detail the derivative of the Ridge bias vector (b / ₑ₈₃₆₄) and the stability of the hardware decommissioning bound (m_ / ₇ₘₒₓ -1733 cycles), proving the extraction veto is a robust, inescapable physical trap. Files Included: main. pdf / main. tex: The definitive UNIFIED PRD manuscript. chameleonₗambertₘapper. py: Open-source Python toolkit (v61. 0. 0) simulating Bounded Sensitivity Derivatives, Trace Conservation, Thermodynamically Anchored Annealing, and Parseval anti-aliasing limits.