argon_full_shell
plain-language theorem explainer
Argon (Z=18) satisfies the closed-shell condition where valence electron count equals period length. Chemists using Recognition Science would cite this to confirm noble gases mark shell completion in the φ-ladder model of atomic radii. The verification reduces directly to evaluating the two defining expressions for valence electrons and period length.
Claim. For argon with atomic number 18, the valence electron count equals the period length: let $v(Z) = Z - c_{prev}(Z)$ and $p(Z) = c_{next}(Z) - c_{prev}(Z)$, then $v(18) = p(18)$.
background
The Chemistry.AtomicRadii module derives atomic radii from φ-ladder scaling. It states that radii decrease across a period as Z increases and increase down a group as new shells appear farther from the nucleus. Noble gases exhibit local maxima because they complete shells. The upstream definitions are valenceElectrons(Z) as electrons beyond the previous noble-gas core and periodLength(Z) as the difference between next and previous closure points. The module doc notes that noble gases are exactly those elements where valence count equals period length.
proof idea
The proof is a one-line wrapper that applies native_decide to compute the equality from the definitions of valenceElectrons and periodLength. No further lemmas or tactics are used.
why it matters
This equality confirms the Recognition Science claim that noble gases occur where valence electrons match period length, anchoring the closed-shell maxima in the φ-ladder radii model. It supports the module's period and group trends for atomic structure. The declaration does not feed further theorems in the current graph but aligns with the T5-T8 forcing steps that fix shell structure and D=3 dimensions.
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