Epistemic Gain in M–Space: A Metric for AI Governance in Complex Systems.

Safety-critical sectors such as power transmission and autonomous mobility are not replacing their deterministic controllers; they are adding artificial intelligence (AI) layers to existing systems to gain additional, sustainable business value. This approach increases the socio-technical complexity, creating pressure for a structured means to compare benefits, oversight effort and risk over time. In this descriptive study, we introduce Epistemic Gain G , a scalar derived from the Δ − η − ζ model that links foresight gains to human oversight and system friction. Within this framework, G > 0 is treated as a necessary condition for epistemically sustainable scaling. We then formulate a conjectured governance-level Law of Diminishing Returns that holds up to a Scaling Failure Threshold, beyond which marginal upgrades begin to destroy value. Drawing on recent empirical studies, we further sketch the Δ − η − ζ model and show how G can be displayed in software development lifecycle dashboards. This paper extends the earlier IEEE AI × B 2025 conference paper in three main directions: (i) provide the theoretical foundation of the M-Vector and formalize it as the explicit epistemic state M (t) underpinning the Δ − η − ζ model; (ii) introducing semantic instability φ and epistemic drift ξ as properties inspired by causal representation learning, used here as an AI-safety and governance lens; and (iii) identifying canonical regions of M -space for deterministic, vital, symbolic, sub-symbolic and generative AI systems. The overarching aim is to formalize the theoretical basis of G and its time-variant machine form, enabling it to serve as a governance indicator for when to scale, optimize, or pause AI deployments. [ABSTRACT FROM AUTHOR]