ionizationProxy
plain-language theorem explainer
ionizationProxy(Z) returns the valence electron count for atomic number Z, yielding a dimensionless proxy for first ionization energy that equals 1 for alkali metals and the full period length for noble gases. Chemists working on periodic trends in the Recognition Science framework cite this definition to derive the sawtooth ionization pattern from φ-ladder scaling. The implementation is a direct one-line alias to the valenceElectrons function.
Claim. For atomic number $Z$, the ionization proxy is defined as the valence electron count $v(Z)$, ranging from 1 (alkali metals) to the period length (noble gases).
background
The Ionization Energy module models first ionization energy $I_1(Z)$ via a sawtooth forced by φ-rail scaling (base energy ~ φ^{2n} for period n) and position within the period. valenceElectrons(Z) is defined as Z minus the previous noble gas closure, counting electrons beyond the closed shell; at noble gases this equals the period length. The module documentation states this proxy captures the cost to break into a forming shell and predicts alkali minima and noble maxima without data fitting.
proof idea
This definition is a one-line wrapper that directly applies the valenceElectrons computation from the PeriodicTable module.
why it matters
This definition supplies the position factor for the theorems alkali_min_ionization, noble_max_ionization, ionization_monotone_within_period, and sawtooth_reset. It realizes the position factor in the φ-ladder scaling of the module documentation, enabling the predicted sawtooth pattern. It connects to the Recognition framework through period lengths derived from the phi fixed point and eight-tick octave structure.
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