chlorine_gt_sodium
plain-language theorem explainer
The declaration shows that the electronegativity ranking for atomic number 17 exceeds that for atomic number 11 under the RS-derived ratio of valence electrons to period length. A chemist verifying periodic trends within the Recognition Science model would cite this as direct confirmation that rankings rise toward shell closure. The proof reduces the comparison to arithmetic by unfolding the four periodic-table definitions and normalizing the resulting fractions.
Claim. The electronegativity ranking of the element with atomic number 17 exceeds that of the element with atomic number 11, where the ranking equals the ratio of valence electrons to the length of the current period.
background
The module treats electronegativity as a consequence of shell structure and distance to noble-gas closure. The ranking function is defined as the ratio of valence electrons to period length, with higher fractions corresponding to stronger electron attraction within the same shell. This matches the module's stated mechanism: EN scales as the inverse distance to the next closure, modulated by shell number, and reproduces the classical Mulliken relation in simplified form.
proof idea
The proof is a one-line wrapper that applies simplification on the definitions of the ranking function, valence-electron count, period length, and the two closure maps, then normalizes the resulting rational numbers to decide the inequality.
why it matters
The result verifies the explicit prediction in the module documentation that electronegativity increases across a period as valence electrons approach closure. It supplies a concrete instance supporting the RS claim that rankings follow fractional shell filling, consistent with the phi-ladder scaling described for CH-008. No downstream theorems currently depend on it.
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