pith. sign in
theorem

cs_valence_one

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

plain-language theorem explainer

Cesium has exactly one valence electron by the Recognition Science definition subtracting the prior noble gas core from atomic number. Chemists modeling alkali metal radii trends in the phi-ladder framework would cite this to anchor group-one behavior. The verification is a direct native computation of the valenceElectrons function at Z=55.

Claim. Cesium (atomic number 55) has one valence electron beyond the previous noble gas core: valence electrons of cesium equal 1.

background

Recognition Science derives atomic radii from phi-ladder scaling of coherence lengths, with period trends decreasing radii across a row and group trends increasing them down a column via new shells. The valenceElectrons function is defined as Z minus prevClosure Z, counting electrons outside the last closed shell; at noble gases this count equals the period length, matching the RS insight that closed shells occur precisely when valence equals period length. The module sets this within CH-007, where effective radii also decrease with valence electrons due to screening penetration.

proof idea

The proof is a one-line wrapper that applies native_decide to evaluate the arithmetic definition of valenceElectrons at 55.

why it matters

This result belongs to the series of alkali-metal valence checks (Li, Na, K, Rb, Cs) that confirm the periodic table structure underlying phi-ladder radius predictions. It supports the module's claim that alkali metals exhibit maximal radii after noble-gas closures because a new shell begins. No downstream theorems are recorded, leaving open whether these facts will be folded into a general radius formula.

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