CriticalPoint
The CriticalPoint structure records the temperature and pressure at which a first-order phase transition terminates, together with a Boolean flag marking the singularity. Researchers modeling J-cost bifurcations in Recognition Science thermodynamics would reference it to locate the endpoint of coexistence curves. The declaration is a plain record definition introducing three fields with no further axioms or computations.
claimA critical point is a triple $(T, P, s)$ with $T, P$ real numbers and $s$ a Boolean, marking the termination of a first-order transition line where the J-cost landscape changes topology.
background
The module derives phase transitions from bifurcations in the J-cost landscape, where multiple local minima merge or split as parameters vary and the system jumps between them. Temperature is defined as the inverse of the Lagrange multiplier beta. Pressure is given by the product of density, the kernel evaluation, and a scaling factor delta. The constant K is defined as the square root of phi, serving as a dimensionless bridge ratio.
proof idea
This is a structure definition that introduces the three fields temperature, pressure, and is_singular without any proof obligations or computational content.
why it matters in Recognition Science
It supplies the data structure for the endpoint of first-order lines within the phase-transition theory built from J-cost bifurcations. The module targets derivation of such transitions as information-theoretic bifurcations, with the attached comment noting possible numerical links such as Tc/Tb ratios near sqrt(3) for water or phi/1.3 for helium. No downstream uses are recorded, leaving the precise embedding into the phi-ladder open.
scope and limits
- Does not compute numerical values for specific substances.
- Does not derive the location of the critical point from the J-cost function.
- Does not enforce thermodynamic relations between the recorded fields.
formal statement (Lean)
126structure CriticalPoint where
127 temperature : ℝ
128 pressure : ℝ
129 is_singular : Bool
130
131/-- φ-connection to critical points?
132
133 Water: Tc/Tb = 647/373 ≈ 1.73 (close to √3 ≈ 1.73)
134 Helium: Tc = 5.2 K, Tb = 4.2 K, Tc/Tb ≈ 1.24 (close to φ/1.3) -/