SolvationShell
plain-language theorem explainer
The declaration enumerates five solvation shells for an ionic solute in water when the configuration dimension equals 5. Modelers of hydration structure in Recognition Science cite it to anchor shell-count and radius-ratio claims. It is realized as an inductive type with five constructors that derives Fintype for immediate cardinality access.
Claim. The type of solvation shells is the inductive type whose constructors are the primary hydration shell, the secondary hydration shell, the tertiary hydration shell, the bulk-boundary layer, and the far bulk region.
background
In the Recognition Science treatment of chemistry the configuration dimension is set to 5 for an ionic solute in water. This yields five canonical shells ordered by distance: primary hydration, secondary hydration, tertiary hydration, bulk-boundary layer, and far bulk. Adjacent shells lie on the phi-ladder so that the radius ratio between consecutive shells equals phi. The inductive definition supplies the finite set whose cardinality is asserted to be exactly 5 in the companion certification structure.
proof idea
The declaration is an inductive definition that introduces five distinct constructors and derives DecidableEq, Repr, BEq, and Fintype in a single line.
why it matters
This definition supplies the finite enumeration required by the downstream certification structure SolvationShellCert, which records that the cardinality equals 5, that adjacent radii satisfy the phi ratio, and that every radius is positive. It realizes the B10 Chemistry Depth claim of five canonical shells with phi-ladder spacing and thereby closes the interface between the configDim parameter and concrete hydration layers.
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