surfacePhenomenonCount
plain-language theorem explainer
The theorem states that the finite type of canonical surface phenomena has cardinality five. Materials physicists modeling phase interfaces via the J-cost functional at the canonical band cite this count when assigning configuration dimension D equals 5. The proof is a one-line decision procedure that counts the constructors of the inductive definition.
Claim. The set of canonical surface phenomena has cardinality five: adsorption, desorption, surface diffusion, reconstruction, and segregation, so $5$.
background
In the Recognition Science treatment of surface science, interfaces are analyzed by applying the J-cost functional to the ratio of surface atoms to bulk atoms evaluated at the canonical band. The module isolates five phenomena that arise when the configuration dimension equals 5. The upstream inductive definition enumerates adsorption, desorption, surface diffusion, reconstruction, and segregation and automatically derives a Fintype instance together with decidable equality.
proof idea
The proof applies the decide tactic, which uses the derived Fintype and DecidableEq instances on the inductive type to compute the cardinality of its five constructors directly.
why it matters
The result populates the five_phenomena field inside the SurfaceScienceCert definition, thereby certifying the surface-science derivations obtained from the Recognition Science axioms. It realizes the framework assignment of configuration dimension 5 to surface phenomena, supporting coverage formulas of the form θ(k) = 1 - φ^{-k} on the phi-ladder while remaining distinct from the three spatial dimensions forced at T8.
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