Ensuring Ethical Stability in Cyber-Physical Systems and Articial Intelligence Decisions: Simulation-Based Validation of the KerimovAlekberli (KA) Framework

Articial intelligence systems deployed in high-stakes environments face a common structural challenge: decision quality degrades under uncertainty, and this degradation is rarely captured by aggregate accuracy metrics. The Kerimov-Alekberli (KA) framework addresses this challenge by modeling stability as an entropy-damped function of utility and internal structural properties. The generalized stability score E∗ = U − S/D, where D = 1 + γIint + λCa, moderates the destabilizing effect of entropy S through two internal structural proxies: internal integration Iint and aligned reective capacity Ca. This paper extends the KA framework in two directions. First, we introduce a generalized ethical score E = αU−βS−γB−δR, incorporating bias/fairness penalty B and regulatory risk R as additional ethical dimensions relevant to nancial, medical, and autonomous system deployment. Second, we validate both formulations across ve simulation environments: (1) a Markov chain stress test across three entropy regimes (n = 1000), (2) an adaptive threshold simulation with time-varying structural proxies (T = 200), (3) a competitor model comparison (n = 500), (4) a proxy interaction analysis across ve correlation levels, and (5) a credit/income classication fairness simulation (n = 5000, test n = 1500). Across all ve environments, the KA framework demonstrates consistent advantages: mean stability gain ∆ = 0 ̄ .040 across entropy regimes (monotonically increasing from 0.022 to 0.075 as entropy rises); 27.4% lower coecient of variation and 55% faster entropy spike recovery than the linear baseline; lowest coecient of variation among interpretable nonlinear models under high-entropy conditions; proxy independence maintained up to ρ(Iint, Ca) = 0.8; and a 28.8% reduction in gender disparity scores in fairness-sensitive classication. These results position the KA framework as a practically deployable, formally grounded stability metric for AI systems operating under uncertainty.