railFactor
plain-language theorem explainer
The rail factor supplies the dimensionless multiplier phi to the power 2n for scaling energies or frequencies on spectral rail n. Chemists and nuclear physicists cite it when building relative band positions on the phi-ladder without element-specific tuning. The definition is a direct real exponentiation of the constant phi.
Claim. For integer rail index $n$, the rail factor equals $phi^{2n}$, where $phi$ is the golden ratio.
background
The Spectral Ladder module supplies basic helpers for cross-domain spectral rails obeying $f_n = f_0 cdot phi^{2n}$ with $f_0 = E_{coh}/h$. The rail factor is the dimensionless shell multiplier $E_n/E_{coh}$ at rail $n$. Upstream results in PeriodicTable and Nuclear.Octave record the identical expression as the default rail multiplier. It draws the constant phi from the CPM Constants bundle.
proof idea
The definition is a one-line wrapper that applies real exponentiation to raise phi to twice the integer rail index.
why it matters
This definition is invoked by railEnergy to obtain dimensionful energies $E_n = E_{coh} cdot phi^{2n}$ and by frequencyOnRail for spectral frequencies. It supplies the basic phi-ladder scaling required for coherence diagnostics in the eight-tick octave and for the Recognition forcing chain step that fixes phi as the self-similar fixed point.
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