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The notation collects the score values from the first sample through sample T. Statistics such as a mean or variance act on a chosen subset of this sequence. A collection of values alone does not specify sample timing or independence.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Φ_t | Score at sample t |
| T | Last included sample index |
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Original context
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While $\Phi$ measures instantaneous consciousness state, we introduce a resonance metric capturing temporal coherence:
\begin{definition}[Resonance]
For consciousness time series $\{\Phi_t\}_{t=1}^T$, resonance at time $T$ is:
\begin{equation}
R_T = \frac{1}{1 + \text{Var}(\{\Phi_t\}_{t=T-w}^T)}
\end{equation}
where $w$ is the window size (typically 1000 ticks).
\end{definition}
Resonance is high when consciousness maintains stable values (low variance) and low when consciousness fluctuates. We establish empirical thresholds:Exact original notation
\{\Phi_t\}_{t=1}^T