Beyond Generative AI: Geometric Stability of Cognitive Systems under the TCFQ-DTS Framework

This paper proposes a rigorous geometric framework for evaluating endogenous structural stability in large-scale cognitive systems, grounded in the Quantum Phase Constitutive Theory (TCFQ). We characterize the transition from stable inference to mimetic collapse through the introduction of the stability parameter S, defined via the quadratic Wasserstein distance (W_ 2^2) between the empirical distribution of cognitive updates (W (t)) and an institutional semantic attractor (ABTT). The attractor is formalized as a Borel probability measure supported on a compact manifold M with effective negative Ricci curvature. We demonstrate that the critical threshold Scrit ≈ 2.14 corresponds to the breakdown of λ-convexity of the associated energy functional in Wasserstein space, marking a universal geometric phase transition toward structural irreversibility. Furthermore,we define an operational reflexivity operator (ˆR) as a temporal phase shift and propose that system governability be studied under the commutation condition [ˆR,ˆH] = 0.