DVE v1.0: Dynamical Viability Engine — Mathematical Foundation for Trajectory Viability in Probabilistic Systems

This report introduces the Dynamical Viability Engine (DVE), a mathematical framework for measuring trajectory viability in probabilistic systems. DVE formalizes the structural principles of the Structural Counterforce Framework (SCF) and the runtime stabilization mechanisms of VEROK-BFD into measurable quantities. The core contribution is the viability index: V = C × R × E where: - C (Continuity): trajectory smoothness- R (Recursion): transformation adaptability- E (Elasticity): intrinsic response capacity DVE establishes a formal condition for governance effectiveness: dT/dP > epsilonᵣ A key result is the identification of the False Stability Zone: a regime where outputs appear stable while structural controllability is lost. This work shifts AI safety from output correctness to trajectory controllability. --- Related works (framework components): - SCF v2: https: //doi. org/10. 5281/zenodo. 19184139- SCF (foundational): https: //doi. org/10. 5281/zenodo. 18876636- VEROK v1–v4: https: //doi. org/10. 5281/zenodo. 18073021 https: //doi. org/10. 5281/zenodo. 18146212 https: //doi. org/10. 5281/zenodo. 18285751 https: //doi. org/10. 5281/zenodo. 18468882