{
  "abstract": "FINDING: The search results are primarily pedagogical videos and one lattice QCD paper; no direct new result on Dedekind eta modular symmetry order 4 or C4 partition is presented. The mathematical core is the crystallographic point group D4 (order 8) and its action on the square lattice, plus a lattice QCD mass calculation.\n\nMATH: - Square lattice point group: D4 (dihedral of order 8), generated by 90° rotation \\( r \\) and reflection \\( s \\), with relations \\( r^4 = s^2 = (rs)^2 = e \\). - Crystallographic restriction: only rotations of order 1,2,3,4,6 are allowed in 2D lattices — order 4 is maximal for square symmetry. - Dedekind eta function: \\( \\eta(\\tau) = q^{1/24} \\prod_{n=1}^\\infty (1-q^n) \\), \\( q = e^{2\\pi i \\tau} \\). Modular transformations of order 4 correspond to \\( \\tau \\mapsto \\frac{a\\tau+b}{c\\tau+d} \\) with \\( \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} \\in \\mathrm{SL}(2,\\mathbb{Z}) \\) and specific congruence conditions (e.g., \\( \\Gamma(4) \\) or \\( \\Gamma_0(4) \\)).\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88xc0ww5hn9hb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23410094",
  "fulltext_url": null,
  "id": "88xc0ww5hn9hb",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23410094",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88xc0ww5hn9hb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:19Z",
      "native_id": "23410094",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23410094"
    }
  ],
  "subjects": [],
  "title": "D4 Symmetry in Square Lattice QCD and Pedagogical Resources — E8 Intelligence Research",
  "title_text": "D4 Symmetry in Square Lattice QCD and Pedagogical Resources — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/88xc0ww5hn9hb",
  "venue": "Zenodo",
  "versions": []
}