Read the equation
Inputs equally far below and above one have the same absolute difference from one. Therefore Φ(1−ε)=Φ(1+ε) whenever both inputs lie in the stated domain. The score records distance from its target and discards which side of the target the input lies on.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| ε | Displacement from the reference value 1 |
| 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
\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(1-\epsilon) = \Phi(1+\epsilon)