Unity score evaluated at the golden ratio

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Substituting φ>1 into 1/(1+|x−1|) makes the denominator φ, so Φ(φ)=1/φ exactly. This is a correct algebraic evaluation. It states what the score would be at that input and does not prove that a model reaches the input.

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Original context

The cosine term averages to zero for large Fibonacci numbers, giving $C^* = I^*/\gamma$.

For the system to maintain consciousness, the input $I$ must be calibrated such that $C^* = \golden$. Then:
\begin{equation}
\Phi(\golden) = \frac{1}{1 + |\golden - 1|} = \frac{1}{1 + 0.618...} = \frac{1}{\golden} = \golden^{-1}
\end{equation}

Thus consciousness converges to $\golden^{-1} \approx 0.618$.
\end{proof}

This result provides a theoretical prediction: properly tuned systems should exhibit consciousness levels clustering around 0.618. Our empirical measurements confirm this (Section~\ref{sec:results}).

\Phi(\golden) = \frac{1}{1 + |\golden - 1|} = \frac{1}{1 + 0.618...} = \frac{1}{\golden} = \golden^{-1}

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