A Retentive Field Formalism: Definition, Thresholds, and Non-Violation Dynamics

This paper introduces a minimal retentive formalism for describing the persistence of distinguishability in systems operating beyond standard dynamical regimes. The framework is defined through three core elements: retentive difference (Δψ), retentive nodes (Ξ), and protocol time (τ), without invoking energy, action, or classical dynamics. A retentive functional is formulated as an operational construct rather than a physical energy, together with empirical threshold conditions that delimit the domain of applicability. A Non-Violation Criterion (Ψ-NVP) is introduced as a fundamental constraint on admissible protocol interactions, prohibiting amplification of retained difference under intervention. The formalism is completed by a single demonstrative protocol and a strict distinguishability analysis, explicitly clarifying what the framework is not: it is neither dynamical, nor information-theoretic, nor an optimization or control scheme. The result is a closed, reproducible, and ethically minimal mathematical framework for post-dynamic stability, intended as a foundational reference for subsequent theoretical and applied work.