{
  "abstract": "We establish the conjecture by de Klerk and Pasechnik (2002), claiming that the semidefinite bounds $\\vartheta^{(r)}(G)(r\\geq 0)$ for the stability number $α(G)$ are exact at $r=α(G)-1$, by exhibiting an explicit sum-of-squares certificate. This certificate allows us to recover a known characterization of the minimizers of the Motzkin-Straus formulation for $1/α(G)$. Additionally, we give sum-of-squares copositivity certificates for the matrices satisfying the Hoffman-Pereira sign condition, a crucial condition for characterizing copositive matrices with $\\{-1,0,1\\}$ entries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01010",
  "author_total": 2,
  "authors": [
    {
      "name": "Jineon Baek"
    },
    {
      "name": "Luis Felipe Vargas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at6822gdt0qtx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01010",
  "fulltext_url": null,
  "id": "at6822gdt0qtx",
  "issns": [],
  "landing_url": "https://laas.hal.science/hal-05834954v1",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
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  "openalex": "W7206203190",
  "pdf_url": "https://arxiv.org/pdf/2609.01010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at6822gdt0qtx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05834954",
      "source": "hal",
      "url": "https://laas.hal.science/hal-05834954v1"
    },
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.01010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman-Pereira Matrices",
  "title_text": "Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman-Pereira Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/at6822gdt0qtx",
  "venue": "HAL",
  "versions": []
}