Beyond the Moment: Temporal Coherence as a Second Dimension of Consciousness

The Consciousness Gradient Index (CGI) has demonstrated utility in tracking momentary consciousness across sleep states, psychedelic experiences, and attentional fluctuations. However, CGI measures only instantaneous richness - the degree of integrated, adaptive processing at a given moment. Human-like consciousness also requires continuity: the threading of moments into a persistent self. This paper introduces τ (tau), a second dimension measuring temporal coherence - the degree to which a system bridges states into continuous experience. The full consciousness profile (CGI, τ) resolves key puzzles: why AI systems with high momentary integration feel "different" rather than conscious in the human sense, why amnesia patients experience rich moments without unified selfhood, and how micro-level integration might combine into macro-level experience. We operationalise τ through three components (memory persistence, self-model stability, narrative integration) and validate the framework using EEG data from sleep studies. Results confirm strong dissociation: from Wake to deep NREM sleep, CGI dropped 95% while τ increased 30% (r = 0.15, p = 0.81). REM sleep showed a distinct pattern with both dimensions reduced. These findings support the central claim that consciousness has (at least) two separable dimensions - richness and continuity - and that full consciousness requires both.