What does this research mean for the field?

Trajectory viability in probabilistic systems can be mathematically quantified using a viability index based on continuity, recursion, and elasticity, which reveals a 'False Stability Zone' where systems appear stable despite losing structural controllability. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

The primary aim is to present a framework for measuring and formalizing trajectory viability in probabilistic contexts.

April 11, 2026Open Access

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

Key Points

The primary aim is to present a framework for measuring and formalizing trajectory viability in probabilistic contexts.
Introduced the Dynamical Viability Engine (DVE) as a mathematical framework.
Formalized structural principles of the Structural Counterforce Framework (SCF).
Derived the viability index as a function of continuity, recursion, and elasticity.
Established conditions for governance effectiveness in probabilistic systems.
Identified the False Stability Zone where outputs seem stable but controllability is lost.
Shifted focus of AI safety from output correctness to trajectory controllability.

Abstract

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

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

Key Points

Abstract

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