Version 2.0 — Corrections and Clarifications This revision addresses five issues identified in the original preprint: Table 1 corrected. Wake tau = 0.0 on the min-max EEG scale (not 3.8 as previously reported). The discrepancy arose because waking neural dynamics are the least temporally regular of the measured states — high attentional variability produces low autocorrelation. This does not indicate low experiential temporal coherence; it reflects a gap between signal regularity and experiential continuity, now discussed explicitly in Limitations. AI CGI values removed. The original included specific CGI values for Claude and GPT-4 without validated methodology. These have been replaced with qualitative predictions. Developing rigorous AI measurement methods is flagged as future work. Cross-species CGI values removed. The (CGI, tau) framework is retained as a conceptual tool, but specific CGI numbers for non-human species have been removed pending resolution of phi operationalisation across substrates. Cross-species tau estimates flagged as illustrative. Section 2.3 now explicitly states these are qualitative estimates, not empirical measurements. Signal-experience gap acknowledged. New material in Limitations addresses the distinction between temporal coherence of neural signals and temporal coherence of experience. The core empirical finding is unchanged: CGI and tau proxies dissociate across sleep stages (r = 0.15), supporting the claim that consciousness has at least two separable dimensions. 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.