{
  "abstract": "FINDING: Rationally homologically fibered knot groups with bi-orderable fundamental groups force the Alexander polynomial to have a positive real root — a topological obstruction linking orderability to spectral properties. | MATH: Let \\(K \\subset Y\\) be a knot in a rational homology 3-sphere, \\(G = \\pi_1(Y \\setminus K)\\). If \\(G\\) is bi-orderable and \\(K\\) is rationally homologically fibered (i.e., the commutator subgroup \\(G'\\) is finitely generated over \\(\\mathbb{Q}\\)), then \\(\\Delta_K(t)\\) has at least one root \\(r \\in \\mathbb{R}_{>0}\\). The group is an HNN extension \\(G = H *_{\\phi}\\) with stable letter \\(t\\), and the Alexander polynomial satisfies \\(\\Delta_K(t) \\sim \\det(t \\cdot \\mathrm{Id} - \\phi_*)\\) up to units. The proof uses the fact that a bi-orderable group admits a Conradian left-order, and the HNN structure forces a real eigenvalue of the monodromy \\(\\phi_*\\) on \\(H_1(G';\\mathbb{Q})\\). | CONNECTION: The positive real root condition is a spectral signature. For a fibered\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/bh3xr0zsy8rms.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447082",
  "fulltext_url": null,
  "id": "bh3xr0zsy8rms",
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  "landing_url": "https://zenodo.org/records/23447082",
  "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": [],
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  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh3xr0zsy8rms.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:47Z",
      "native_id": "23447082",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23447082"
    }
  ],
  "subjects": [],
  "title": "Bi-orderable knot groups force positive real roots in Alexander polynomials — E8 Intelligence Research",
  "title_text": "Bi-orderable knot groups force positive real roots in Alexander polynomials — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:47Z",
  "url": "https://research.draconitic.com/paper/bh3xr0zsy8rms",
  "venue": "Zenodo",
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}