predictedI1_eV
plain-language theorem explainer
The definition computes the predicted first ionization energy in eV for atomic number Z by anchoring to the universal coherence energy E_coh and multiplying by the dimensionless φ-scaled factor. Chemists or RS modelers would cite it when extracting numerical values for the sawtooth pattern across the periodic table. The implementation is a direct one-line arithmetic expression that applies scaledIonization and applies the unit conversion factor of 1000.
Claim. The predicted first ionization energy in eV is given by $E_0(Z) = E_{coh} · I_{scaled}(Z) · 1000$, where $I_{scaled}(Z) = φ^{2p} · (v / l)$ with $p$ the period of Z, $v$ the valence, and $l$ the period length.
background
The module derives ionization energies from φ-ladder scaling under the P0-A2 framework. Base energy follows φ^{2n} for period n, position within a period increases toward closure, and subshell blocks carry fixed φ-packing offsets. The upstream scaledIonization definition supplies the dimensionless factor: it multiplies the rail factor φ raised to twice the period by the normalized term (valence divided by period length). Constants.E_coh from the CPM bundle acts as the universal energy anchor, while the module documentation states that alkali metals realize the minimum and noble gases the maximum per period.
proof idea
This is a one-line definition that applies scaledIonization to the input Z, multiplies the result by Constants.E_coh, and scales by 1000 to place the output in the eV range.
why it matters
The definition supplies the quantitative seam for the sawtooth ionization ordering required by the φ-rail scaling in the Recognition Science chain. It directly supports the subsequent ordering theorems that establish alkali minima and noble-gas maxima within each period without data fitting. The construction inherits the self-similar fixed point and eight-tick octave structure from the upstream forcing chain, closing the display interface for the chemistry predictions.
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