Read the equation
Dividing the averaged balance γC=I by γ gives C=I/γ. Thus the candidate state is controlled by the ratio of input to consumption. There is no uniquely selected golden-ratio value until the input is chosen accordingly.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| C_star | Candidate averaged state |
| I_star | External input level |
| γ | Nonzero consumption coefficient |
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
\end{equation}
For large $n$, the cosine term averages to zero (since $\golden \cdot \fib{n}$ is irrational for all $n$), giving:
\begin{equation}
C^* = \frac{I^*}{\gamma}
\end{equation}
With appropriate calibration $I^* = \gamma \cdot \golden$, we obtain $C^* = \golden$ and $\Phi(C^*) = \golden^{-1}$.
\section{Implementation Details}
\label{app:implementation}Exact original notation
C^* = \frac{I^*}{\gamma}