radiusProxy
plain-language theorem explainer
Atomic radius proxy for atomic number Z is the product of the shell radius proxy and the screening factor. Researchers modeling periodic trends under Recognition Science scaling would cite this when deriving effective radii from φ-ladder shell structure. The definition is a direct one-line product of two sibling functions with no additional reduction.
Claim. The atomic radius proxy for atomic number $Z$ is $r(Z) = r_0(Z) · s(Z)$, where $r_0(Z) = φ^{n(Z)}$ is the raw shell radius with shell number $n(Z)$ and $s(Z)$ is the screening factor that reduces the radius as valence electrons increase relative to period length.
background
The module derives atomic radii from φ-ladder scaling under CH-007. Shell radius proxy supplies the base size as $φ$ raised to the shell number, while screening factor supplies the correction $1 - v/(2p)$ where $v$ is valence electrons and $p$ is period length (or 1 when period length is zero). Upstream period definition supplies the φ^k scaling used for shell indices. The local setting states that radii decrease across a period due to increasing Z and increase down a group due to new shells.
proof idea
One-line definition that multiplies shellRadiusProxy Z by screeningFactor Z.
why it matters
This definition supplies the concrete radius expression that realizes the RS mechanism of base φ^n scaling plus valence screening in CH-007. It directly supports the stated predictions of local maxima for noble gases and alkali metals after closed shells. No downstream theorems are recorded, leaving its integration into mass or complexity anchors open.
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