carbon_intermediate
plain-language theorem explainer
Carbon (Z=6) has electronegativity ranking exactly 1/2 under the RS definition. Periodic table modelers cite this to anchor the half-filled shell at the midpoint of the valence fraction scale. The proof unfolds the ranking ratio and evaluates the concrete integers for period 2.
Claim. The electronegativity ranking for carbon satisfies $v(6)/p(6)=1/2$, where $v(Z)$ denotes valence electrons beyond the prior noble-gas core and $p(Z)$ denotes the length of the current period.
background
Electronegativity ranking is the ratio of valence electrons to period length. Valence electrons equal Z minus the previous closure (0 for Z=1-2, 2 for Z=3-10, etc.). Period length is next closure minus previous closure, yielding 8 for the second period containing carbon. The module frames this ratio as a proxy for the classical Mulliken scale EN ~ sqrt(IE x EA), with RS predicting monotonic increase across each period toward shell closure.
proof idea
One-line wrapper that unfolds enRanking together with valenceElectrons, periodLength, prevClosure and nextClosure, then applies numerical normalization to the resulting rational expression.
why it matters
The result supplies the explicit midpoint instance for the second period, confirming the module's claim that EN increases across a period. It instantiates the general ranking definition inside the φ-ladder scaling of CH-008 and supports downstream ordering statements such as fluorine greater than carbon. No parent theorem is recorded in the used-by graph.
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