SecondOrderTransition
plain-language theorem explainer
SecondOrderTransition records the critical exponents and universality class that label continuous phase transitions arising from smooth J-cost minima merging. Condensed-matter physicists classifying singularities such as the Curie point or superfluidity would cite it when mapping J-cost geometry to divergent susceptibilities. The declaration is a bare structure definition with no attached computation or lemmas.
Claim. A second-order transition consists of a list of critical exponents (such as $α, β, γ, ν, …$) together with a universality-class label (Ising, XY, Heisenberg, …).
background
In Recognition Science, phase transitions are J-cost bifurcations: the cost function, defined as the derived cost of a multiplicative recognizer’s comparator or equivalently as the J-cost of any recognition event, measures recognition effort on positive ratios. The upstream from theorem in PrimitiveDistinction supplies the seven-axiom foundation that yields the four structural conditions plus three definitional facts under which these costs are well-defined. The module THERMO-006 therefore treats first-order transitions as discontinuous jumps between distinct minima and second-order transitions as continuous passages through a single flattened minimum.
proof idea
The declaration is a structure definition that directly records the critical exponents as a list of reals and the universality class as a string, with no lemmas or tactics applied.
why it matters
This definition supplies the data container for second-order transitions inside the J-cost bifurcation theory of module THERMO-006. It supports the paper proposition that phase transitions are information-theoretic bifurcations and sits alongside FirstOrderTransition and CriticalPoint in the same module. The structure encodes the scaling data that must ultimately emerge from the Recognition Composition Law and the phi-ladder, although no explicit reduction to T5–T8 is performed here.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.