Disclosure note (Public-safe draft). This document states a minimal, inspectable theorem schema for invariant-gated evolution. Operational thresholds, tuning constants, and any proprietary enforcement parameters are intentionally omitted. This paper presents a minimal, domain-agnostic stability theorem for adaptive systems based on invariant-gated governed evolution. We formalize a setting in which unconstrained update dynamics generically exhibit long-horizon drift or divergence, and show that introducing an explicit admissibility gate—defined by invariant tolerances and a Lyapunov descent condition—guarantees bounded evolution and stability for all time. The result establishes that such a gate is not a heuristic or design preference, but a necessary and sufficient structural condition for stability in adaptive systems. The theorem is constructive at the level of operators and invariants, yet deliberately omits implementation-specific mechanisms, parameterizations, or optimization strategies. This separation allows the stability result to be inspected, critiqued, and applied across domains—including control theory, dynamical systems, and AI inference—without disclosing operational details. The work reframes safety and stability as properties of update geometry and constraint enforcement, rather than training objectives or external policy layers, and provides a mathematical foundation for inference-time governance in long-horizon adaptive systems.

@misc{Morrison2025InvariantGated, title = {Invariant-Gated Governed Evolution: A Minimal Stability Theorem for Adaptive Systems}, author = {Morrison, Kemar Armando}, year = {2025}, doi = {10.5281/zenodo.18181758}, url = {https://doi.org/10.5281/zenodo.18181758}, abstract = {A formal theorem proving that long-horizon stability in adaptive systems requires invariant-gated updates, using Lyapunov descent and bounded invariants, without retraining or reward coupling.}}