Chemistry Phase Diagram Triple From Jcost Matter Phase

MatterPhase in the framework

In the Recognition Science framework, the declaration MatterPhase is a formal list of five states of matter: solid, liquid, gas, plasma, and supercritical. The framework's machine-checked library of formal theorems proves that this list has exactly five members, by a direct check. The declaration also bundles that count with a certificate that the recognition cost function J reaches its minimum value of zero at the equilibrium ratio r = 1.

The framework's picture of a phase diagram starts with its core idea: a recognition event is a discrete record of one thing matching another, and the cost of that match is forced by the framework's axioms. For a substance, the solid, liquid, and gas phases are treated as three competing recognizers. The triple point, the one temperature and pressure where all three phases coexist, is the unique state where each phase's recognition ratio equals 1, so J = 0 for all three at once. The framework proves that this simultaneous minimum is unique: at any other state, at least one phase has positive cost.

This is a structural claim about the framework's model, not a measurement of any actual chemical. The declaration does not compute the triple point of water, carbon dioxide, or any real substance. It does not derive the pressure or temperature values on a real phase diagram. It does not claim that plasma or supercritical states are handled by the same equilibrium argument; only phases 1 through 3, solid, liquid, and gas, enter the triple-point story. The five-state list is a definitional choice, and the uniqueness theorem is about the cost function's minimum, not about laboratory data.

theorem phaseCount : Fintype.card MatterPhase = 5 := by decide

structure PhaseDiagramCert where
  five_phases : Fintype.card MatterPhase = 5
  equilibrium_threshold : CanonicalCert

inductive MatterPhase where
  | solid | liquid | gas | plasma | supercritical
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

No real substance's triple point is computed or predicted. No claim that plasma or supercritical phases satisfy the same equilibrium condition as solid, liquid, and gas. The declaration does not state that the five-phase list is physically exhaustive for all matter.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/PhaseDiagramTripleFromJCost.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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