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

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…