THE TRIDENT A Formal Factorization of Epistemic Coupling and Drift Detection Derivation, Formal Specification, and Applicability Conditions

This paper derives and formally specifies the Trident, a regime-bounded factorization of epistemic coupling designed to detect concealed drift between a model and its domain. Drift is defined as invisible decoupling: divergence of predictions from the domain without immediate detection. The Trident decomposes epistemic coupling into three necessary and sufficient conditions — Representation (variable sanctification), Correction (feedback adequacy), and Calibration (confidence proportionality) — and demonstrates both non-overlap and exhaustiveness of the resulting failure modes. The instrument distinguishes concealed failure from visible error, formalizes applicability conditions (observable state variables, feedback closure feasibility, and claim–test separability), and establishes a failure hierarchy prioritizing representation integrity. The derivation is structurally independent of domain examples and is grounded in the admissibility criterion articulated in Invariance-Weighted Compression under Constraint (DOI: 10.5281/zenodo.18764956). Domain-agnostic instantiations are provided across scientific theory construction, institutional governance, AI alignment, and organizational cognition. The Trident functions not as a general error detector but as a sentinel for invisible epistemic drift within detectable regimes. Keywords epistemic coupling, drift detection, concealed failure, variable sanctification, feedback adequacy, calibration transparency, representation integrity, regime-bounded, non-overlap, exhaustiveness, failure hierarchy, applicability conditions, frame admissibility, invariance-weighted compression, model audit, governance drift, AI alignment, scientific methodology