{
  "abstract": "We give three explicit finite-volume hyperbolic Coxeter lattices in dimension four whose adjoint trace fields are not totally real. They are the reflection groups of the Ma--Zheng polytopes $P_{11,6}$, $P_{11,7}$, $P_{11,8}$. The obstruction is contained in two cyclic products of the doubled unit-normal Gram matrix $A=2G$. Those products recover elements $s=\\sqrt5$ and $u$ satisfying $$ (s-1)u^2+2(s-3)u+s-7=0. $$ After the embedding $s\\mapsto-\\sqrt5$, this quadratic has discriminant $8(1-\\sqrt5)<0$. The cyclic-product field therefore has a complex place. Vinberg's identification of that field with the adjoint trace field and the Emery--Mila total-reality obstruction imply that the three lattices are not pseudo-arithmetic. Torsion-free orientation-preserving finite-index subgroups yield orientable noncompact finite-volume hyperbolic $4$-manifolds with the same obstruction. Exact computations check the census data and provide independent field and finite-volume certificates. A pinned Lean~4 development verifies the radical identity and the number-field obstruction. It also checks the lattice and manifold implications conditional on explicit geometric and literature hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05795",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Kolpakov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45v4pzzhsmyhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05795",
  "fulltext_url": null,
  "id": "45v4pzzhsmyhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05795",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45v4pzzhsmyhz.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds",
  "title_text": "Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/45v4pzzhsmyhz",
  "venue": "arXiv",
  "versions": []
}