HGST E7: Frustration Ordering in Non-Abelian Gauge Theory

Author: Boonsup Waikham
Affiliation: College of Computing, Khon Kaen University, Khon Kaen, Thailand
ORCID: 0009-0000-7693-7295

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Overview

This repository contains the Python simulation code and LaTeX paper source for two companion papers (both accepted, 2026):

[Theory] Hierarchical Graded Structure Theory: Axiomatic Foundations, the Grade-Difference Group, and Non-Abelian Frustration Ordering in Classical Lattice Gauge Extensions E1–E7
Boonsup Waikham, College of Computing, Khon Kaen University

[Empirical] Frustration Universality in Hierarchical Graded Structure Theory: A Lattice Study of the E7 MIXED Class from U(1) to the SU(3)×SU(2)×U(1) Gauge Group
Boonsup Waikham, College of Computing, Khon Kaen University

We measure the HGST MIXED frustration fraction $R$ — the fraction of sign-inconsistent holonomy triads — across four gauge groups on classical 2D lattices, with finite-size scaling (FSS) to the thermodynamic limit.

Principal results

Gauge group	$R_\infty$	Status
U(1)	0	Falsified
SU(2)	$0.3598 \pm 0.0041$	Validated (5-pt FSS)
SU(3)	$0.3539 \pm 0.0195$	Validated
SM C-scalar	$0.4981 \pm 0.0056$	Validated
SM N-scalar	$0.4980 \pm 0.0076$	Validated

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Repository structure

HGST-E7/
├── simulation/          Python physics modules (26 files)
│   ├── su2.py           SU(2) algebra: Haar random, small perturbation
│   ├── su3.py           SU(3) algebra: expm-based
│   ├── u1.py            U(1) — Abelian baseline
│   ├── lattice.py       Lattice2D: sites, edges, plaquettes, BFS
│   ├── fields.py        Link and matter field initialization
│   ├── action.py        Wilson gauge + hopping action, ΔS functions
│   ├── observables.py   R observable via BFS holonomies
│   ├── updates.py       Metropolis sweep (links + matter)
│   ├── simulation.py    SimConfig dataclass, run_point(), FSS utilities
│   ├── su2_l10_colab.py ★ Self-contained Colab-ready SU(2) L=10 script
│   ├── su2_longrun_fss.py  Long-run FSS analysis (L=4–12, seeds 99–102)
│   ├── sm_*.py          Standard Model (SU(3)×SU(2)×U(1)) modules
│   └── ...
│
├── data/                JSON result files (all production runs)
│   ├── su2_l10_summary.json   SU(2) L=10 FSS result
│   ├── su2_L12_b8.json         SU(2) L=12 production run (R=0.3521±0.00089)
│   ├── p1_su3_fss_corrected.json
│   ├── p1_sm_fss_corrected.json
│   └── ...
│
├── arxiv_submit_theory/   LaTeX source — theory paper (Revision 4, ACCEPTED)
│   ├── main.tex           Axiomatic foundations, grade-difference group, E1–E7
│   ├── main.bbl           Pre-generated bibliography (required by arXiv)
│   ├── references.bib
│   └── figures/
│
├── arxiv_submit_empirical/ LaTeX source — empirical paper (Revision 4, ACCEPTED)
│   ├── main.tex           FSS lattice study, U(1)→SM gauge groups
│   ├── main.bbl
│   ├── references.bib
│   └── figures/
│
├── paper/               Working LaTeX drafts and reviewer response
│
├── notebooks/
│   └── vacation_analysis.ipynb
│
├── .env.example         Author/ORCID template → copy to .env (not committed)
├── .gitignore
├── requirements.txt
├── CITATION.cff         Machine-readable citation metadata
└── UPLOAD_PLAN.md       arXiv / Zenodo upload checklist

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Quick start

# 1. Install dependencies
pip install -r requirements.txt      # numpy + scipy only

# 2. Run SU(2) L=10 FSS (standalone, no local imports)
python simulation/su2_l10_colab.py
# → writes su2_l10_summary.json + su2_l10_runlog.json
# Runtime: ~15 min on a modern laptop (L=10, 500 measurements)

Run in Google Colab

1. Upload simulation/su2_l10_colab.py to the Colab session
2. !python su2_l10_colab.py
3. Download su2_l10_summary.json for results

Reproduce SU(3) FSS (4-point, L=4,6,8,10)

cd simulation
python run_simulation.py --gauge su3 --L 4 6 8 10 --beta 8.0 --kappa 0.3

Reproduce SM scan

cd simulation
python sm_scan.py --L 4 6 8 --beta3 8.0 --beta2 4.0 --kappa 0.3

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All JSON files in data/ are the actual production outputs used in the paper.
Simulation seeds are fixed (SEED=203 for SU(2) L=10; see each script header).
The paper PDFs can be recompiled separately:

cd paper
# For Theory:
pdflatex Theoretical_Framework && bibtex Theoretical_Framework && pdflatex Theoretical_Framework
# For Empirical:
pdflatex Empirical_Study && bibtex Empirical_Study && pdflatex Empirical_Study

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Citation

If you use this code, please cite:

@software{waikham_hgst_e7_2026,
  author    = {Waikham, Boonsup},
  title     = {HGST E7: Simulation Code for Frustration Ordering
               in Non-Abelian Gauge Theory},
  year      = {2026},
  version   = {4.0.0},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.18873889},
  url       = {https://github.com/boonsup/hgst-e7}
}

See also CITATION.cff for machine-readable metadata.

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License

MIT — see LICENSE.