{
  "abstract": "The Skolem--Mahler--Lech Theorem asserts that a non-degenerate linear recurrence sequence (LRS) has only finitely many zeros, but is ineffective in the sense that no general procedure is known to determine them. In this paper a \\emph{pseudo-effective} approach is introduced: rather than seeking effective bounds for every sequence, one obtains explicit bounds valid for all but a controlled number of sequences of bounded height, up to a natural equivalence. Such results are established for order $3$ LRS's, and extended to all higher orders subject to suitable height constraints on the characteristic roots. The underlying mechanism is a quantitative theory for exponential-polynomial equations subject to low-height multiplicative perturbations. In particular, it is shown that the finiteness phenomenon underlying the Skolem--Mahler--Lech Theorem persists under arithmetic perturbations whose height is permitted to grow linearly at a sufficiently small rate. As a further application, a moving-target finiteness result is established for linear orbits entering expanding arithmetic neighbourhoods of proper linear subspaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32901",
  "author_total": 1,
  "authors": [
    {
      "name": "Victor Shirandami"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ppgehr1sc0m1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32901",
  "fulltext_url": null,
  "id": "4ppgehr1sc0m1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32901",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214756080",
  "pdf_url": "https://arxiv.org/pdf/2609.32901",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ppgehr1sc0m1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32901",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32901"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Pseudo-Effectivity in the Skolem-Mahler-Lech Theorem",
  "title_text": "Pseudo-Effectivity in the Skolem-Mahler-Lech Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4ppgehr1sc0m1",
  "venue": "arXiv",
  "versions": []
}