The Paton Operator Set A Minimal Operational Framework for Admissible Continuation with Companion Practical Guide

This record contains two connected documents forming a unified operational release within the Paton System. The first paper “The Paton Operator Set” defines a minimal operational framework for admissible continuation. It formalises the core operators required to evaluate whether a system state may persist under constraint and how continuation is structurally governed. The framework reduces system operation to admissibility gated transitions ensuring that only constraint-compatible states are permitted to propagate. The second document “The Paton Operator Set — How to Use It” provides a practical guide to applying the operator set. It translates the formal structure into usable steps demonstrating how systems can be evaluated stabilised and guided through admissible trajectories without requiring advanced mathematical training. Together these documents establish both the formal operational structure and its direct application. The operator set defines the minimal mechanism through which admissibility is evaluated and enforced across transitions while the companion demonstrates how this mechanism is used in practice. This release extends the Paton System from structural description to operational deployment providing a domain-neutral method for assessing continuation filtering trajectories and maintaining system stability under constraint. The framework introduces no new domain-specific laws and does not replace existing models. It operates as a pre-theoretical layer determining whether continuation is permitted before domain-specific dynamics apply.