{
  "abstract": "The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially‐filled tensors subject to rank conditions. The identifiability of points on secant varieties has also been a topic of much research in algebraic geometry. It is often formulated as the problem of identifying a set of points satisfying a given set of algebraic relations. A key question then is to prove sufficient conditions for relations to guarantee the identifiability of the points. This paper proposes a new general framework for capturing the identifiability problem when a set of algebraic relations has a combinatorial structure and develops tools to analyse the impact of the underlying combinatorics on the local or global identifiability of points. Our framework is built on the language of graph rigidity, where the measurements are Euclidean distances between two points, but applicable in the generality of hypergraphs with arbitrary algebraic measurements. We establish necessary and sufficient (hyper)graph‐theoretical conditions for identifiability by exploiting techniques from graph rigidity theory and algebraic geometry of secant varieties. In particular our work analyses combinatorially the effect of non‐generic projections of secant varieties.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematical and Statistical Sciences University of Galway Galway Ireland",
    "Departments of Mathematics and Computer Science KU Leuven Leuven Belgium",
    "School of Mathematical Sciences Lancaster University Lancaster UK",
    "Department of Business Economics Tokyo University of Science Tokyo Japan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "James G. Cruickshank",
      "orcid": "0000-0003-4731-9302"
    },
    {
      "affs": [
        1
      ],
      "name": "Fatemeh Mohammadi",
      "orcid": "0000-0001-5187-0995"
    },
    {
      "affs": [
        2
      ],
      "name": "Anthony Nixon",
      "orcid": "0000-0003-0639-1295"
    },
    {
      "affs": [
        3
      ],
      "name": "Shin‐ichi Tanigawa",
      "orcid": "0000-0002-6834-8017"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9r787em58b19z.bib",
  "cited_by": 16,
  "doi": "10.1112/jlms.70633",
  "fulltext_url": null,
  "id": "9r787em58b19z",
  "issns": [
    "0024-6107",
    "1469-7750"
  ],
  "landing_url": "https://doi.org/10.1112/jlms.70633",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W4378945367",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "Wiley",
  "ris": "https://research.draconitic.com/paper/9r787em58b19z.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:36Z",
      "native_id": "W4378945367",
      "source": "openalex",
      "url": "https://doi.org/10.1112/jlms.70633"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2605|Tensor decomposition and applications",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Identifiability of points and rigidity of hypergraphs under algebraic constraints",
  "title_text": "Identifiability of points and rigidity of hypergraphs under algebraic constraints",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/9r787em58b19z",
  "venue": "Journal of the London Mathematical Society",
  "versions": []
}