{
  "abstract": "Matrix Hilbert series retain local elementary-divisor data that their determinants discard. For locally finite positively graded elementary algebras whose vertex simples are of type $FP_\\infty$ and whose matrix Hilbert series is rational, we construct from possibly infinite minimal resolutions a rational Euler matrix and its signed local Smith profile at $x=1$. The profile refines pole-order growth for perfect modules and is invariant under shift-compatible graded Morita and perfect-derived equivalences. Every finite integer profile occurs, while a wholly negative profile forces exponential corner growth. This extends the nonnegative local Smith framework for twisted Calabi--Yau algebras to a setting in which the Euler matrix may itself have poles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35248",
  "author_total": 1,
  "authors": [
    {
      "name": "Atabey Kaygun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zb7ks6b6ahx5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35248",
  "fulltext_url": null,
  "id": "1zb7ks6b6ahx5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35248",
  "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.RA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214723970",
  "pdf_url": "https://arxiv.org/pdf/2609.35248",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zb7ks6b6ahx5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35248",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35248"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Signed Euler--Smith Profiles of Graded Algebras",
  "title_text": "Signed Euler--Smith Profiles of Graded Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1zb7ks6b6ahx5",
  "venue": "arXiv",
  "versions": []
}