k_valence_one
plain-language theorem explainer
Potassium with atomic number 19 has exactly one valence electron under the definition that subtracts the prior noble gas core from Z. Researchers verifying alkali metal positions in Recognition Science atomic radius models would cite this result to anchor group trends. The verification reduces to direct evaluation of the valence count function via native computation.
Claim. For the element with atomic number 19 the valence electron count, defined as the difference from the preceding noble gas closure, equals 1: $v(19)=1$.
background
Atomic radii follow shell structure in Recognition Science, with base radius scaling as phi to the shell number. Radii decrease across periods from rising Z and increase down groups from new shells farther from the nucleus, per the module setting on phi-ladder scaling and coherence length.
proof idea
The proof is a one-line wrapper that applies native_decide to the valenceElectrons definition, which subtracts prevClosure(19) from 19 to obtain 1.
why it matters
This anchors the alkali metal series in the chemistry module, confirming radius maxima after noble gases from new shell initiation. It supports the RS mechanism for radii scaling with shell number and valence screening, fitting the period and group trends outlined in the module.
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