{
  "abstract": "The templex is a topological object bridging homologies and templates for chaotic dynamics. This article places the templex within category theory, introducing a directed path algebra, an edge operator on directed paths, and an equivalence relation for directed cycles that is distinct from directed homologies. The resulting functorial invariants are of two kinds: Abelian-group invariants, namely the homology groups, and semigroup invariants, namely the generatex semigroups. These invariants are separable through forgetful functors and constitute a robust framework for identifying tipping points, disambiguating physical mechanisms, and benchmarking data-driven models against observations or simulations. The formulation sets forth a nonmetric criterion for chaos from finite-time data and reveals that the concatenable nature of topological modes of variability is a direct consequence of the semigroup structure of the directed path algebra. Two applications are presented: an experimental speech signal and a climatic numerical simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2602.18463",
  "author_total": 1,
  "authors": [
    {
      "name": "Denisse Sciamarella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bf83cp0e3hm8x.bib",
  "cited_by": 0,
  "doi": "10.1103/zx76-5115",
  "fulltext_url": null,
  "id": "bf83cp0e3hm8x",
  "issns": [
    "2470-0045",
    "2470-0053"
  ],
  "landing_url": "https://hal.science/hal-05759679v1",
  "language": "en",
  "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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      "1703|Topological and Geometric Data Analysis"
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  "pdf_url": "https://hal.science/hal-05759679/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-10",
  "publisher": "American Physical Society (APS)",
  "ris": "https://research.draconitic.com/paper/bf83cp0e3hm8x.ris",
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    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05759679",
      "source": "hal",
      "url": "https://hal.science/hal-05759679v1"
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  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "hal:2.sdu.stu.cl",
      "subfield": "climate"
    },
    {
      "field": "earth",
      "origin": "hal:1.sdu.ocean",
      "subfield": "oceanography"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-at",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:0.nlin",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Functorial invariants for chaos topology from data",
  "title_text": "Functorial invariants for chaos topology from data",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/bf83cp0e3hm8x",
  "venue": "Physical Review E",
  "versions": []
}