rb_valence_one
plain-language theorem explainer
Rubidium with atomic number 37 has exactly one valence electron under the Recognition Science definition that subtracts the prior noble gas core from Z. Chemists modeling periodic trends or phi-ladder atomic radii would cite this specific alkali-metal case to anchor group trends. The proof evaluates the definition directly via native decision procedure on the arithmetic difference.
Claim. For the element with atomic number 37, the number of electrons beyond the previous noble gas core equals 1: valence count(37) = 1.
background
The module derives atomic radii from phi-ladder scaling and predicts that radii decrease across a period with rising Z while increasing down a group with new shells. Valence electrons are defined as the count beyond the previous noble gas core, with the key insight that noble gases complete shells precisely when this count equals the period length. This supplies the concrete instance for rubidium as an alkali metal that begins a new shell after a noble gas.
proof idea
One-line wrapper that applies native_decide to evaluate the difference Z minus prevClosure Z at input 37.
why it matters
This anchors the alkali-metal valence count inside the CH-007 atomic-radii predictions, confirming the group trend of radius increase down the series. It supports the broader Recognition Science claim that shell number sets the base radius via phi scaling. No downstream uses are recorded, leaving the result as a computational checkpoint rather than a lemma feeding further theorems.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.