surfaceScienceCert
plain-language theorem explainer
The declaration supplies a concrete certificate that Recognition Science yields precisely five canonical surface phenomena at interfaces. Surface scientists modeling adsorption, desorption, diffusion, reconstruction and segregation would cite it when linking the J-functional to coverage on the phi-ladder. The definition is a direct record constructor that inserts the decidable cardinality theorem into the required structure field.
Claim. The surface science certificate is the structure instance asserting that the finite type of canonical surface phenomena has cardinality five, obtained by substituting the explicit enumeration theorem into the single field of the certificate structure.
background
In the Recognition Science treatment of surfaces, interface energy is expressed via the J-cost functional applied to the ratio of surface to bulk atoms at the canonical energy band. The module enumerates five canonical phenomena—adsorption, desorption, surface diffusion, surface reconstruction and surface segregation—whose count equals the configuration dimension D = 5. The upstream theorem surfacePhenomenonCount establishes this count by exhaustive enumeration and decision. The structure SurfaceScienceCert packages the equality Fintype.card SurfacePhenomenon = 5 as a reusable certificate.
proof idea
The definition is a one-line record constructor that directly assigns the theorem surfacePhenomenonCount to the five_phenomena field of the SurfaceScienceCert structure.
why it matters
This definition closes the surface-science fragment of the Recognition Science derivation by supplying an explicit Lean witness for the five-phenomena claim. It aligns with the framework's use of configuration dimension to fix the number of surface processes, consistent with the eight-tick octave and spatial dimension D = 3 in the broader forcing chain. No downstream theorems yet consume the certificate, leaving open its integration into explicit energy calculations or coverage formulas on the phi-ladder.
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