normalizedEA
plain-language theorem explainer
Normalized electron affinity for atomic number Z is the ratio of distance to next noble gas closure over period length, or zero when the period length is zero, producing a value in the half-open unit interval that ranks electron addition favorability. Recognition Science chemists would cite this proxy when deriving periodic trends from the approach-to-closure cost reduction. The definition implements the ratio through a direct conditional that guards the division by the period length.
Claim. For atomic number $Z$, the normalized electron affinity equals the distance to next noble gas closure divided by the period length when the period length is positive, and equals zero otherwise.
background
The module models electron affinity via the Recognition Science mechanism of cost reduction toward eight-tick shell neutrality. Electron affinity is high for halogens one electron short of closure and near zero or negative for noble gases at closure. The definition normalizes the raw distance proxy to enable cross-period comparison on the unit interval.
proof idea
The definition is a one-line wrapper that applies a case split on whether periodLength Z equals zero. It returns zero in that case and otherwise casts both the distance to closure and the period length to reals before dividing.
why it matters
This supplies the normalized proxy that formalizes the CH-006 predictions of halogen maxima and noble-gas minima within each period. It links the periodic table structure to the eight-tick octave and the forcing chain through the closure distance. No downstream uses appear yet, leaving open its integration with mass-ladder or Berry-threshold results.
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