The Cognitive Autonomy Index: An Operational Framework for Detecting Recursive Cognitive Transitions in AI Systems

This paper introduces the Cognitive Autonomy Index (CAI), a composite operational metric designed to detect recursive cognitive transitions (RCTs) in AI systems. The CAI integrates three measurable components: (1) KL divergence over consecutive model states to quantify belief revision magnitude, (2) workspace activation to measure integration coherence, and (3) CalibrationGain to assess metacognitive quality. A system crosses the cognitive singularity threshold (TCST) when all three components simultaneously exceed empirically calibrated bounds, triggering a mandatory fail-closed Hard Gate that halts autonomous operation pending human review. Three controlled simulations illustrate the framework's expected behavior and failure modes under toy conditions. A Recurrence-Guided Attention proxy module (RQAA) provides preliminary proxy evidence of measurable divergence signals near putative transition boundaries, with boundary shift signals 12–25× stronger than within-regime baselines. We explicitly bound our claims: the framework does not detect consciousness or sentience; TCST is not a universal constant and requires per-system empirical calibration; current simulations are proof-of-concept only. The contribution is operational: a formally specified, falsifiable, and instrumentable criterion set for identifying recursive cognitive transitions, formalized within the Cognitive Singularity Theory (CST) research program.