shellRadius
plain-language theorem explainer
shellRadius assigns to each natural number k the real value phi raised to k, supplying the base radii for the five solvation shells around an ionic solute. Solvation chemists working with configDim D=5 hydration layers cite it for the geometric progression with fixed ratio phi. The declaration is a direct power assignment with no additional computation or hypotheses.
Claim. The radius of the k-th solvation shell is given by $r_k = phi^k$.
background
The module treats solvation shells for an ionic solute in water under configDim D=5, listing five layers: primary hydration, secondary hydration, tertiary hydration, bulk-boundary layer, and far bulk. Shell radii lie on the phi-ladder so that the ratio between adjacent shells equals phi. The definition supplies the radius function that later results invoke for positivity and ratio properties.
proof idea
The declaration is a direct definition that equates shellRadius k to the power phi^k.
why it matters
This definition supplies the radius function required by SolvationShellCert, which records five shells, the phi ratio for every consecutive pair, and strict positivity. It also feeds shellRadius_ratio and shellRadius_pos, and is referenced by screeningFactor and shellRadiusProxy in AtomicRadii. The construction realizes the phi-ladder step inside the Recognition Science chemistry layer, consistent with the self-similar fixed point from the forcing chain.
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