distToClosure
plain-language theorem explainer
distToClosure(Z) equals the number of electrons needed to reach the next noble gas shell closure for atomic number Z. Chemists modeling electron affinity in the Recognition Science framework cite it as the basic proxy for how favorable electron addition becomes. The definition is a direct one-line alias to the upstream distToNextClosure computation.
Claim. For atomic number $Z$, the distance to next noble gas closure is $d(Z) := n(Z) - Z$, where $n(Z)$ is the atomic number of the next shell closure.
background
The Electron Affinity module models EA via proximity to noble gas closure, following the RS prediction that halogens (one electron short) show high affinity while noble gases (at closure) show near-zero or negative values. Upstream definitions supply the pieces: distToNextClosure(Z) := nextClosure(Z) - Z, valenceElectrons(Z) := Z - prevClosure(Z), and periodLength(Z) := nextClosure(Z) - prevClosure(Z). These capture the approach-to-closure pattern inside each period.
proof idea
One-line wrapper that applies distToNextClosure: the body is exactly distToNextClosure Z.
why it matters
This supplies the core distance that feeds eaProxy, halogen_ea_one (proxy equals 1), noble_gas_ea_zero (proxy equals 0), and ea_decreases_within_period. It realizes the CH-006 claim that EA ordering follows shell-filling progress toward 8-tick neutrality. The definition therefore links the periodic table structure to the Recognition Science 8-tick octave.
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