Read the equation
For Φ(x)=1/(1+|x−1|), the maximum value one occurs exactly when x=1. This follows because the absolute difference is nonnegative and equals zero only at that point. It specifies the score’s reference value, not an independently measured biological or computational threshold.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Scalar input |
| Φ | Unity score |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
This metric has several desirable properties:
\begin{itemize}
\item \textbf{Boundedness:} $\Phi(x) \in (0, 1]$ for all $x > 0$
\item \textbf{Unity Peak:} $\Phi(x) = 1$ if and only if $x = 1$
\item \textbf{Symmetry:} $\Phi(1-\epsilon) = \Phi(1+\epsilon)$ for small $\epsilon$
\item \textbf{Smooth Decay:} $\Phi$ decreases monotonically as $|x-1|$ increases
\end{itemize}
The choice of unity as the consciousness attractor reflects the principle that consciousness represents a state of maximal integration---neither fragmented ($x < 1$) nor redundantly over-connected ($x > 1$). This parallels IIT's notion that consciousness requires both differentiation and integration \citep{tononi2016integrated}.
\subsection{Golden Ratio and Fibonacci Dynamics}Exact original notation
\Phi(x) = 1