PhaseCoexistenceTopology
plain-language theorem explainer
Recognition Science chemistry models employ an inductive enumeration of five phase-coexistence topologies to capture all J-cost driven equilibria. The topologies are binodal for two-phase separation, eutectic for three-phase, peritectic for four-phase, plus azeotrope and tricritical point. This definition supplies the finite set whose cardinality is certified as exactly five by a subsequent theorem. It is introduced as a plain inductive type deriving Fintype, which immediately yields the cardinality result used downstream.
Claim. The phase coexistence topologies consist of five elements: the binodal (two-phase coexistence), eutectic (three-phase), peritectic (four-phase), azeotrope, and tricritical point.
background
In the module on Phase Coexistence from J-Cost, five canonical phase-coexistence topologies are defined, corresponding to configDim D = 5. These include the two-phase binodal, three-phase eutectic, four-phase peritectic, azeotrope, and tricritical point. Binodal curvature is gated by the canonical J(φ) band on the chemical-potential ratio. The module states Lean status: 0 sorry, 0 axiom.
proof idea
The declaration is a direct inductive definition listing the five constructors, with derivations for DecidableEq, Repr, BEq, and Fintype to support downstream cardinality proofs.
why it matters
This definition provides the finite set of topologies that PhaseCoexistenceCert and phaseTopology_count rely on to assert Fintype.card = 5. It fills the role of fixing the configuration dimension D = 5 in the chemistry module, linking J-cost minimization to the five standard thermodynamic topologies.
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