ColloidRegime
plain-language theorem explainer
ColloidRegime enumerates the five canonical colloidal stability regimes obtained from J-cost analysis. Soft-matter physicists cite it when classifying DLVO potentials or confirming the configDim D=5 count. The declaration is a direct inductive definition that automatically supplies decidable equality and finite type structure.
Claim. Let $R$ be the inductive type whose five constructors are electrostatic stabilization, steric stabilization, depletion stabilization, gel formation, and flocculation. The type is equipped with decidable equality, a representation, Boolean equality, and finite type structure.
background
The module derives colloidal stability from the J-cost functional of Recognition Science. J-cost quantifies recognition defect between particle configurations, and the DLVO secondary minimum corresponds to a canonical band in the J($phi$) potential ratio. The five regimes are identified with configDim D = 5 in this soft-matter setting.
proof idea
The declaration is a direct inductive definition. No lemmas are applied and no tactics are required; the derived instances for DecidableEq, Repr, BEq, and Fintype are generated automatically by the Lean kernel.
why it matters
The definition supplies the enumeration required by the downstream theorem colloidRegime_count, which proves Fintype.card ColloidRegime = 5, and by the structure ColloidStabilityCert that packages the same cardinality fact. It completes the soft-matter depth of the framework by linking J-cost bands to the five observable colloidal phases listed in the module documentation.
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