solvationShellCert
plain-language theorem explainer
This definition assembles a certificate asserting exactly five solvation shells whose radii form a geometric progression with common ratio phi. A chemist working on ionic hydration layers would cite the certificate to confirm the shell count and scaling for configDim equal to five. The construction is a direct record assembly that pulls the cardinality from the decision theorem and the two radius properties from their respective lemmas.
Claim. Let a solvation-shell certificate be the structure requiring that the number of shells equals five, that consecutive radii satisfy $r_{k+1}/r_k=phi$ for every natural number $k$, and that every radius is strictly positive. The definition supplies an element of this structure whose cardinality field is the theorem establishing the count five, whose ratio field is the theorem establishing the golden-ratio scaling, and whose positivity field is the theorem establishing that every radius exceeds zero.
background
The module treats five canonical solvation shells for an ionic solute in water when the configuration dimension equals five: primary hydration, secondary hydration, tertiary hydration, bulk-boundary layer, and far bulk. Shell radii lie on the phi-ladder with adjacent-shell ratio equal to phi. The local setting is the B10 chemistry depth whose Lean status is zero sorry and zero axiom.
proof idea
The definition is a direct record construction supplying the three fields of the certificate structure. It obtains the cardinality field from the solvationShell_count theorem, the ratio field from the shellRadius_ratio theorem, and the positivity field from the shellRadius_pos theorem.
why it matters
The definition supplies the concrete witness required by the SolvationShellCert structure inside the chemistry module. It closes the B10 chemistry depth by exhibiting the five shells with phi-scaled radii for configDim equal to five. No downstream uses are recorded; the declaration stands as the canonical witness for the solvation-shell model.
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