pith. sign in
theorem

fluorine_gt_b

proved
show as:
module
IndisputableMonolith.Chemistry.Electronegativity
domain
Chemistry
line
58 · github
papers citing
none yet

plain-language theorem explainer

Fluorine (Z=9) has higher electronegativity ranking than boron (Z=5) under the Recognition Science definition. Chemists using the phi-ladder model for period-wise trends would cite this when confirming that EN rises toward shell closure. The proof is a one-line term wrapper that unfolds the ranking, valence, and closure functions then reduces the inequality by norm_num.

Claim. Let $r(Z)$ be the electronegativity ranking of atomic number $Z$, given by the ratio of valence electrons to period length. Then $r(9) > r(5)$.

background

Electronegativity ranking is defined as valenceElectrons(Z) divided by periodLength(Z). Valence electrons equal Z minus the previous noble-gas closure; period length is the difference between next and previous closures. These functions encode shell structure so that higher valence fraction within a period signals stronger electron attraction, approximating the classical Mulliken relation via distance to closure.

proof idea

The proof is a one-line term wrapper. It applies simp to unfold enRanking together with valenceElectrons, periodLength, prevClosure and nextClosure, then invokes norm_num to compare the resulting concrete rationals.

why it matters

The result supplies a concrete instance of the module prediction that EN increases across a period as atoms approach noble-gas closure. It supports sibling statements such as en_increases_across_period and group_17_en_order. In the larger Recognition Science setting it ties chemical ordering to the same phi-ladder and eight-tick octave used for mass and force derivations.

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