{
  "abstract": "FINDING: Modular arithmetic is foundational to cryptography and connects to lattice structures in higher-dimensional geometry, but the provided sources are mostly pedagogical videos—no new mathematical discovery is presented. | MATH: Modular arithmetic: a ≡ b (mod n) ⇔ n | (a − b). Key operations: (a + b) mod n, (a × b) mod n. Cryptographic relevance: finite cyclic groups Z/nZ, discrete logarithm problem, and multiplicative inverses exist iff gcd(a, n) = 1. The one research-level item (arXiv:0706.3841) concerns arithmetic lattices in hyperbolic spaces—these are discrete subgroups of Lie groups with algebraic number-theoretic origins. | CONNECTION: Arithmetic lattices are intimately tied to root systems (e.g., A_n, B_n, C_n, D_n) and Weyl groups—crystallographic symmetries. The golden ratio φ = 1.618 appears in the geometry of hyperbolic 3-manifolds (e.g., the figure-eight knot complement has volume related to Lobachevsky function at π/3, not directly φ, but arithmetic lattices often ha\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"
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  "bibtex": "https://research.draconitic.com/paper/56v4w8k02rgh3.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526361",
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  "id": "56v4w8k02rgh3",
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  "language": "eng",
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  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56v4w8k02rgh3.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:49Z",
      "native_id": "23526361",
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  "title": "Modular Arithmetic's Cryptographic Role and Geometric Lattice Links: A Pedagogical Review — E8 Intelligence Research",
  "title_text": "Modular Arithmetic's Cryptographic Role and Geometric Lattice Links: A Pedagogical Review — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:49Z",
  "url": "https://research.draconitic.com/paper/56v4w8k02rgh3",
  "venue": "Zenodo",
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