Operator 5: Endogenous Variable Latency Calibration Operator Strict Mathematical Specification, Derivation, and Verification

Within the framework of Status-Relational Entropy (SRE) dynamics, the deployment of raw discrete connectivity metrics induces severe localized horizon fragmentation and zero-degree vacuum singularities across asynchronous distributed cuts. To secure systemic causality and data tractability, this paper develops and formalizes Operator 5, the Endogenous Variable Latency Calibration Operator ($\\mathcal{M}_{\\text{latency}}$). Adhering to the No-Dimension Principle, the proposed operator executes Relativistic Dimensional Reduction by mapping topological path-overlap invariants onto micro-scale discrete penetration rates along directed boundary propagation channels. To prevent arithmetic exceptions in vacuum layers, we establish a rigidly clamped explicit formulation using an infinitesimal floating-point protection variable and an endogenous vacuum propagation speed constant bound by mutually interlocked topological cycles. Furthermore, to defend against high-frequency side-channel differential manipulation, the sampling routines are cryptographically isolated within a zero-measure sub-manifold of the chain complex image space. We mathematically prove via the Irreconstructibility Theorem that the supremum of the total variation distance for any finite-sample empirical model approaches unity, thereby invalidating any retrospective parameter reconstruction. Numerical validation suites demonstrate that the operator successfully triggers an adaptive logarithmic dilation of micro-pulse iteration overhead under dense topological clusters while strictly guaranteeing a decoupled, constant operational overhead of $\\mathcal{O}(1)$ across expanding macroscopic horizons.