{
  "abstract": "We classify regular cyclic scalar invariants of non-degenerate hyperbolic ${\\mathcal N}=1$ spin supertriangles which are additive under geodesic subdivision. After fixing the spin lift, the common-first gauge (introduced in earlier work by the second-named author and further developed here) gives a complete $3|4$ modulus of such supertriangles.. The space of additive scalar invariants is proved to have superdimension $3|1$: ordinary hyperbolic area in degree zero, two even generators in degree two, and one odd generator in degree three; the degree-one and degree-four sectors vanish. One degree-two generator is the fermionic first variation of body area, equivalently the nilpotent correction from ordinary body angle defect to super angle defect. The degree-three generator changes sign under reversal of the spin lift, while the other generators are fixed, so ordinary supertriangles carry only three even invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23209",
  "author_total": 2,
  "authors": [
    {
      "name": "Ilia Gaiur"
    },
    {
      "name": "Robert Penner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ezjd10jna6fj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23209",
  "fulltext_url": null,
  "id": "5ezjd10jna6fj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23209",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7222938545",
  "pdf_url": "https://arxiv.org/pdf/2610.23209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ezjd10jna6fj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regular Additive Scalar Invariants of ${\\mathcal N}=1$ Hyperbolic Spin Supertriangles",
  "title_text": "Regular Additive Scalar Invariants of 𝒩=1 Hyperbolic Spin Supertriangles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/5ezjd10jna6fj",
  "venue": "arXiv",
  "versions": []
}