{
  "abstract": "FINDING: Heegner numbers (d = −1, −2, −3, −7, −11, −19, −43, −67, −163) are the only negative discriminants with class number h(−d) = 1, yielding integer j-invariants at imaginary quadratic points; recent work extends moments of class numbers for indefinite forms and Ramanujan-type series tied to d = 163. | MATH: Class number h(−d)=1 for d ∈ {1,2,3,7,11,19,43,67,163}. j((1+√−163)/2) = −640320³ = −262537412640768000 (integer). Ramanujan series: 1/π = (√163/8) Σ_{n=0}^∞ ( (6n)! / (n!)³ ) · (545140134n + 13591409) / (640320³)^{n+1/2}. Moment asymptotics: Σ_{d>0, ε_d ≤ x} h(d)^k ~ C_k x^{2k+1} (log x)^{−?} (per arXiv:1609.01630). | CONNECTION: 163 ≈ 0.618 × 264 (φ-linked? No — but 163 = 4×40.75, not golden). However, 640320³ = (2⁶·3·5·23·29)³ — factors align with 2,3,5 (base-60 primes). j-invariant values at Heegner discriminants are algebraic integers; for d = −163, the j-value is an integer whose prime factorization includes 2⁶·3³·5³·23³·29³ — all primes ≤ 29, echoing crystallographic ro\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/8fbg1s5ms7bt8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23616838",
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  "id": "8fbg1s5ms7bt8",
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  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fbg1s5ms7bt8.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:48Z",
      "native_id": "23616838",
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      "url": "https://zenodo.org/records/23616838"
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  "title": "Heegner Numbers and Integer j-Invariants: Class Number One and Ramanujan Series — E8 Intelligence Research",
  "title_text": "Heegner Numbers and Integer j-Invariants: Class Number One and Ramanujan Series — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:48Z",
  "url": "https://research.draconitic.com/paper/8fbg1s5ms7bt8",
  "venue": "Zenodo",
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}