{
  "abstract": "We study holomorphic functions on permutation-invariant subsets of an infinite-dimensional sequence space that are invariant under all finite permutations of coordinates. Working on domains modeled on the space $\\czero$ of null sequences, we show that permutation symmetry forces the first differential to vanish along every constant tail: the coordinate derivatives agree there and an averaging argument annihilates their common value. This yields rigidity---constancy---on domains of constant sequences, and more generally on any $\\cc$-chain-connected domain on which the differential vanishes on the finitely supported directions. The method has a sharp boundary: a precise obstruction prevents the elementary argument from reaching the finitely many exceptional coordinates of a non-constant point, so unconditional rigidity on general eventually-constant domains remains open. In the other direction, an explicit example---any Banach limit on $\\ell^\\infty$---shows that the chain-connectedness and boundedness hypotheses cannot be dropped: mere topological connectedness admits non-constant symmetric entire functions. We record the vector-valued corollary and discuss the motivating application to holomorphic cross-sections of the zero-set map, isolating the lifting problem that remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20196",
  "author_total": 2,
  "authors": [
    {
      "name": "David Feldman"
    },
    {
      "name": "Jon Bannon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ay9m0kvjk872.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20196",
  "fulltext_url": null,
  "id": "8ay9m0kvjk872",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20196",
  "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.CV"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213580111",
  "pdf_url": "https://arxiv.org/pdf/2609.20196",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ay9m0kvjk872.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20196",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20196"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rigidity of symmetric holomorphic functions on infinite-dimensional sequence spaces",
  "title_text": "Rigidity of symmetric holomorphic functions on infinite-dimensional sequence spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/8ay9m0kvjk872",
  "venue": "arXiv",
  "versions": []
}