phaseCoexistenceCert
plain-language theorem explainer
The declaration supplies a concrete certificate asserting exactly five phase-coexistence topologies under the J-cost model. Chemists classifying multicomponent diagrams would cite it when enumerating binodals, eutectics, peritectics, azeotropes, and tricritical points. It is realized as a direct assignment of the topology count obtained from a decidable enumeration.
Claim. Let $C$ be the structure requiring that the cardinality of the set of phase-coexistence topologies equals five. The definition witnesses $C$ by setting the topology count equal to the result of the enumeration theorem.
background
Phase coexistence is governed by the J-cost functional satisfying the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The module lists five canonical topologies for configDim $D=5$: two-phase binodal, three-phase eutectic, four-phase peritectic, azeotrope, and tricritical point, with binodal curvature controlled by the canonical $J(φ)$ band on chemical-potential ratios. The upstream structure formalizes the cardinality requirement as a field inside the certificate. The supporting theorem establishes the count by direct decision.
proof idea
The definition is a one-line wrapper that populates the topology-count field of the certificate structure using the result of the decidable enumeration theorem.
why it matters
This definition completes the enumeration of phase-coexistence topologies required by J-cost thermodynamics in the chemistry module. It supplies the base certificate for downstream modeling of multicomponent diagrams inside the Recognition Science framework, where J-uniqueness (T5) and the eight-tick octave (T7) constrain allowed configurations. The count is fully decidable, so no open scaffolding remains.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.