fluorine_gt_n
plain-language theorem explainer
The declaration establishes that fluorine (Z=9) has a higher electronegativity ranking than nitrogen (Z=7) under the Recognition Science definition. Chemists applying phi-ladder shell scaling to predict reactivity trends would cite this ordering to confirm the expected rise across the second period. The proof is a one-line term that unfolds the ranking definition and resolves the inequality by numerical normalization.
Claim. The electronegativity ranking of fluorine exceeds that of nitrogen, where the ranking for atomic number $Z$ is the ratio of valence electrons to period length.
background
Electronegativity ranking is defined as valenceElectrons(Z) divided by periodLength(Z). Valence electrons equal Z minus the previous noble gas closure, while period length is the difference between next and previous closures. This ratio implements the module's mechanism that higher valence fraction signals stronger electron attraction within a shell. The module sets electronegativity patterns from phi-ladder scaling of shell structures, with classical Mulliken form recovered approximately as the inverse distance to next closure modulated by shell number.
proof idea
The proof is a one-line term that applies simp to unfold enRanking together with valenceElectrons, periodLength, prevClosure and nextClosure, then uses norm_num to evaluate the resulting arithmetic comparison between the two atomic numbers.
why it matters
This result fills one concrete instance of the module's prediction that electronegativity increases across a period toward closure. It supports the listed key predictions for fluorine having the highest value and for the general trend of rising EN with valence fraction. No downstream theorems are recorded, leaving open the integration with full reactivity models or the phi-ladder mass formula.
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