Simulating the Kerimov-Alekberli Stability Framework: Four Mechanistic Validation Studies of an Entropy-Damped Stability Score for Large Language Models

The Kerimov-Alekberli (KA) stability framework proposes a generalized ethical-stability score, E* = U - S/D, where D = 1 + gamma I_int + lambda C_a. The denominator D dampens the destabilizing effect of entropy S through two structural proxies: internal integration I_int and aligned reflective capacity C_a. Earlier results showed that E* exceeds the linear baseline E = U - S on the IST-20 benchmark, but three questions remained unresolved: whether damping generalizes across entropy regimes, whether E* adapts to time-varying structural states, and whether it outperforms structurally distinct scoring models under high entropy. This paper addresses these questions through four simulation studies. Simulation 1, based on a Markov chain with n = 1000 observations, validates the damping mechanism across three entropy states. The mean difference Delta = E* - E is 0.0400 (p < 0.001 in both paired t-test and Wilcoxon test), increasing from State A (0.022) through State B (0.047) to State C (0.075), with a near-perfect association between Delta and entropy, r = 0.9968. Simulation 2, using an adaptive threshold over T = 200 steps, shows that E* is 27.4 percent less variable than E (CV = 0.073 versus 0.100) and recovers from entropy spikes faster (5 versus 11 steps). Simulation 3, comparing four scoring models with n = 500 observations, shows that E* achieves the lowest coefficient of variation under high-entropy conditions (S > 0.15) while preserving interpretability through entropy damping. Simulation 4 shows that I_int and C_a carry complementary information when their mutual correlation rho(I_int,C_a) is below 0.8, but become partially redundant above this threshold. Overall, the simulations provide mechanistic validation of the KA framework beyond aggregate benchmark statistics and identify directions for future empirical and theoretical work.