{
  "abstract": "FINDING: Search results are dominated by pedagogical videos on Fourier/DFT fundamentals, with one substantive paper on a quadratic discrete Fourier transform (QDFT) and mutually unbiased bases (MUBs). No direct quasicrystal diffraction proof is retrieved. | MATH: QDFT generalizes standard DFT via quadratic phase factors: \\( F_Q(k) = \\sum_{n=0}^{N-1} f(n) \\, e^{2\\pi i (a n^2 + b n)/N} \\) (implied by \"quadratic\" in finite fields/rings); MUBs in dimension \\(d\\) exist in sets of \\(d+1\\) bases, tied to prime-power dimensions and the discrete Fourier transform matrix \\( F_{jk} = \\frac{1}{\\sqrt{d}} e^{2\\pi i jk/d} \\). No explicit irrational frequency ratio or discrete spectrum constant appears. | CONNECTION: Weak — QDFT relates to finite geometries and symplectic structures over \\(\\mathbb{Z}_N\\), which underpin root systems \\(A_n\\) and certain crystallographic lattices, but no golden ratio or base-60 link is present in retrieved text. | DEPTH: 2 — The material is introductory or tangential; t\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/6q0tbhx9x9wgc.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635345",
  "fulltext_url": null,
  "id": "6q0tbhx9x9wgc",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23635345",
  "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": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6q0tbhx9x9wgc.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635345",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635345"
    }
  ],
  "subjects": [],
  "title": "Gap in Quasicrystal Diffraction Proofs: QDFT and MUBs Dominate Search Results — E8 Intelligence Research",
  "title_text": "Gap in Quasicrystal Diffraction Proofs: QDFT and MUBs Dominate Search Results — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/6q0tbhx9x9wgc",
  "venue": "Zenodo",
  "versions": []
}