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Method

Problem target

This topic studies whether UET-style transition rules can reproduce selected critical-point and order-parameter benchmarks.

Core components

Engine components

Code/01_Engine/Engine_Phase.py

Proof-oriented components

Code/02_Proof/Proof_Order_Parameter.py

Research and comparison components

Code/03_Research/Research_Critical_Exponents.py
Code/03_Research/test_05_phase_demixing.py
Code/03_Research/test_phase_transitions.py

Variable framing

Primary modeled quantities: critical temperature, order parameter, critical exponents, and transition-scale quantities
Formula registry: see FORMULA_AUDIT.md for the distinction between selected exponent benchmarks, normalized Cahn-Hilliard dynamics, order-parameter diagnostics, and future material-data gates.

Assumptions

The topic is currently a phenomenological comparison package tied to selected critical-point datasets.

Domain of validity

Selected fluids and materials transition benchmarks represented in topic-local files.

Excluded cases

A general renormalization-group derivation for all transition classes.

Parameter sensitivity note

Critical exponents and fit settings remain dependent on the chosen benchmark subset.
The current primary verifier is deliberately narrow: it checks only the beta critical exponent for a 3D Ising/liquid-gas benchmark.
Cahn-Hilliard simulations should be treated as normalized mechanism diagnostics until seed, grid, morphology, and material-unit gates are added.

Dependency policy

0.4_Superconductivity_Superfluids may reuse this topic's transition language only as a mechanism analogy until material-specific gates exist.
0.13_Thermodynamic_Bridge may reference critical behavior only with the selected-exponent limitation.
0.0_Grand_Unification should index this topic as a selected benchmark plus normalized mechanism model, not a full universality proof.