0.11_Phase_Transitions

layout	article
title	UET Topic 0.11: Phase Transitions
description	Critical-exponent benchmark and normalized phase-transition dynamics in the UET framework.

0.11 Phase Transitions

Note

AI-Digest: This topic currently supports an internal benchmark for the 3D Ising/liquid-gas beta critical exponent and contains normalized spectral Cahn-Hilliard phase-separation simulations. It does not yet establish a full renormalization-group derivation or universal phase-transition theory.

Current Claim Boundary

The primary verifier compares the current UET beta-exponent projection against a topic-local 3D Ising/liquid-gas benchmark. The Cahn-Hilliard solver and order-parameter proof scripts are mechanism diagnostics until their nondimensional units, seeds, morphology metrics, and material baselines are locked.

Conceptual Diagram

flowchart LR
    A["critical_exponents.json"] --> B["beta_exp and beta_theory"]
    C["UET beta projection"] --> D["relative beta error"]
    B --> D
    D --> E["primary artifact"]
    F["Cahn-Hilliard engine"] --> G["order and domain diagnostics"]
    G --> H["future morphology gate"]
    I["NIST critical points"] --> J["future material-data gate"]

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Evidence Matrix

Layer	Current status	Evidence / artifact	Claim allowed
Beta critical exponent	Primary internal benchmark	Result/artifacts/0_11_phase_transitions_verification.json	selected exponent compatibility
Cahn-Hilliard dynamics	Normalized model exists	Engine_Phase.py, FORMULA_AUDIT.md	mechanism simulation
Order parameter proof	Simulation diagnostic	Proof_Order_Parameter.py	internal order-emergence check
NIST critical points	Working-copy data only	Data/NIST_Critical_Points.csv	future provenance/data gate
Universal phase-transition theory	Not closed	limitations and formula audit	do not claim full proof

5x4 Grid Structure

Pillar	Purpose
Doc/	analysis notes for symmetry breaking, phase separation, and critical behavior
Ref/	critical exponent, Cahn-Hilliard, Ginzburg-Landau, and thermodynamic references
Data/	topic-local critical exponent and critical-point working copies
Code/	engine, proof, research, competitor, and visualization scripts
Result/	artifacts, plots, and run logs

Quick Start

cd C:\Users\santa\Desktop\uet_harness
python docs/topics/0.11_Phase_Transitions/Code/03_Research/Research_Critical_Exponents.py

Key Files

• FORMULA_AUDIT.md: formula, unit, constant, proof-status, and failure-mode registry.
• VERIFICATION_SPEC.md: primary command, metrics, thresholds, and artifact interpretation.
• DATA_MANIFEST.md: current data roles and provenance gaps.
• METHOD.md: topic method scope and dependency policy.
• LIMITATIONS.md: blockers that prevent stronger claims.

Current Limitations

• The primary benchmark currently tests beta only, not the full critical-exponent set.
• The Cahn-Hilliard solver is normalized and not yet calibrated to a material dataset.
• Order-parameter thresholds are internal diagnostics.
• Upstream provenance for critical-exponent and critical-point tables still needs a stronger external data cache.

Status note: internal critical-exponent benchmark and formula-audit hardening gate.