enRanking
plain-language theorem explainer
A simplified electronegativity proxy for atomic number Z is supplied as the ratio of valence electrons to the length of its period. Chemists working within the Recognition Science framework would cite it to derive ordering predictions such as fluorine having higher ranking than lithium or carbon being intermediate. The definition is a direct case distinction that returns zero for degenerate periods and otherwise the normalized valence count.
Claim. For atomic number $Z$, the electronegativity ranking equals $v(Z)/p(Z)$ where $v(Z)$ is the number of valence electrons beyond the previous noble gas core and $p(Z)$ is the period length, or zero if the period length vanishes.
background
The module develops electronegativity predictions from the Recognition Science φ-ladder scaling. Electronegativity measures an atom's tendency to attract electrons, with RS predicting patterns based on shell structure and distance to closure. The classical Mulliken relation is replaced by a mechanism based on distToNextClosure inverse modulated by shell number, yielding forecasts that fluorine ranks highest while noble gases rank low and rankings rise across periods but fall down groups.
proof idea
The definition is a direct conditional expression. It checks whether periodLength Z equals zero and returns 0 in that case; otherwise it casts valenceElectrons Z and periodLength Z to reals and divides them.
why it matters
This proxy underpins the comparison theorems throughout the module, including fluorine_gt_be, cesium_low_en, and carbon_intermediate. It realizes the CH-008 key prediction that electronegativity increases across a period as valence electrons approach shell closure. In the Recognition Science context it links to the eight-tick octave by using period length as a measure of shell capacity derived from closure points in the forcing chain.
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