A Unified Formalism for Constraint-Driven Convergence: Energy, Governance, and the Calculus of Attractor Redirection

Five mathematical frameworks — statistical mechanics (Boltzmann, 1877), Lyapunov control theory (Lyapunov, 1892), information geometry (Kullback & Leibler, 1951), energy-based machine learning (LeCun et al. , 2006), and computational thermodynamics (Landauer, 1961) — developed largely in parallel, each arrived at a version of the same computable condition. This paper places them in explicit conversation and shows that the condition takes the form of a single ratio: Γ = Δ / (Eₕigh − Edrift) with threshold Γ > 1. In every documented failure cited in this paper — Knight Capital (440M, 2012), the Flash Crash (1T, 2010), cancer (18M diagnoses annually), LLM jailbreaking, and the 2003 Northeast Blackout — Γ was less than 1. This paper does not claim to have discovered a new law. It claims that an existing law — already accepted in five fields — has not been stated in the form that makes its governance implications visible. We state it in that form, derive four theorems, provide estimation pipelines for computing Γ in real systems, and show what it would have taken to prevent what happened. This paper is the mathematical companion to Pre-Stabilisation Dynamics: A Process-First Ontology for Drift, Formation, and Governance in Complex Systems (Balasubramanian, 2026). DOI: 10. 5281/zenodo. 19190423