{
  "abstract": "We construct explicit algebraic finite Gabor windows that are simultaneously full spark and phase retrievable, with quantitative control of the self-ambiguity function. In every cyclic dimension, a constant--Chu window has an exactly computable ambiguity minimum of order $N^{-3/2}$; for $N\\ge25$, a two-site Chu repair has margin comparable to $dN^{-3/2}$ for every divisor $d\\le\\sqrt N$. A quantitative algebraic regularization, based on the high-degree specialization principle used in explicit full-spark Gabor constructions, imposes full spark while retaining a fixed proportion of a seed's ambiguity margin. These ingredients give explicit simultaneous constructions in every cyclic dimension and a factor-sensitive improvement when $N$ has a divisor near $\\sqrt N$. Further consequences include exact Chinese-remainder tensorization, optimal-order squarefree families, near-SIC prime regularization, lifted stability, and a finite cyclic Schrödinger construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09614",
  "author_total": 1,
  "authors": [
    {
      "name": "Dongwei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1sxz09rkqsr83.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09614",
  "fulltext_url": null,
  "id": "1sxz09rkqsr83",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09614",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212154495",
  "pdf_url": "https://arxiv.org/pdf/2609.09614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1sxz09rkqsr83.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.09614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09614"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval",
  "title_text": "Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/1sxz09rkqsr83",
  "venue": "arXiv",
  "versions": []
}