The Cognitive Singularity Theory (CST) - A Proposed Measurement Framework for Recursive Cognitive Transitions (V.7.0)

The Cognitive Singularity Theory (CST) proposes a conceptual framework to identify the operational regime boundary where an AI system transitions from static pattern-matching to recursive self-modification. We introduce the Cognitive Autonomy Index (CAI), a composite metric integrating belief revision magnitude, workspace coherence, and calibration-gated metacognitive monitoring via an exponentially weighted moving average (EWMA) formulation. A fail-closed Hard Gate protocol requires verifiable calibration improvement before attributing autonomy. The threshold (TCST) is defined non-circularly via an independent regime indicator R (t) and change-point detection. The paper outlines three preliminary simulations (paradigm shift, HOT proxy sanity check, Goodhart probe), a Trust Model for externalized monitoring, and State-Aware Alignment for conditioning preference learning on cognitive state quality.