VTF-01 — Synkyria as an Operator-and-Witness Extension of Viability Theory under Finite Capacity

Abstract

This paper introduces Synkyria as an operator-and-witness extension of classical viability theory under finite capacity. Classical viability theory examines whether trajectories can remain within an admissible set over a specified horizon, utilising concepts such as viability kernels and set invariance. Synkyria preserves this mathematical backbone, but adds an architectural accountability layer required under finite horizons and bounded execution. The central shift is from existence-only viability — “can a trajectory remain in K?” — to accountable viability: “can admissibility remain operative, witness-legible, temporally situated, and reviewable under finite capacity?” The paper develops this extension through five structural additions: (i) a minimal transition grammar of ACCEPT, REFUSE, HOLD/DELAY, and RE-DESCRIBE as an availability condition under finitude; (ii) operator semantics for boundary governance and scale transition; (iii) an AEW architectural basis coupling Admissibility, Execution, and Witness as the minimal unit of accountable viability; (iv) an operational-temporal layer in which witness timing, trace history, and carried admissibility-relevant residues matter; and (v) portability across levels through admissibility- and witness-consistent re-description. The result is not a controller, algorithm, or domain-specific implementation. It is a structural necessity account of what must be available and legible in any auditable finite-horizon viability regime under bounded execution. The paper positions Synkyria in relation to classical viability theory, control barrier functions, constrained Markov decision processes, safe reinforcement learning, and runtime verification, while clarifying the additional role of witness, refusal, holding, re-description, and operational temporality. This record belongs to the Viability-Theoretic Foundations (VTF) series of the Synkyria Project. Series: Viability-Theoretic Foundations (VTF)Series code: VTF-01

Topics & Concepts