{
  "abstract": "We interpret the convolution constructions of [arXiv:2604.26357] in Hodge-theoretic terms, extending the Hodge defect calculation of [arXiv:2609.19341]. For Hodge--Tate modules on $\\mathbb C^*$ smooth outside $1$, the defect is the action of an element of the Deligne--Terasoma transport algebra expressed through the Drinfeld associator. For convolutions of iterated Kummer extensions, comparison of mixed Hodge structures produces a beta factor and yields the regularized double shuffle relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21356",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikita Markarian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vn3v93h64mvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21356",
  "fulltext_url": null,
  "id": "0vn3v93h64mvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21356",
  "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.AG"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7213940488",
  "pdf_url": "https://arxiv.org/pdf/2609.21356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vn3v93h64mvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Double shuffle relations via the Hodge defect",
  "title_text": "Double shuffle relations via the Hodge defect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/0vn3v93h64mvh",
  "venue": "arXiv",
  "versions": []
}