{
  "abstract": "Building on a construction of Weifeng Yang, we present a simplified counterexample to Rockafellar's sum conjecture on $c_0(\\N_0\\times\\N)$. The central observation is geometric: the domain of a maximally monotone operator can have a nonconvex norm closure. In our example, this gives a short proof that the operator is not of type (FPV), which in turn implies the failure of the sum conjecture. We define an explicit operator using geometric series and provide a detailed proof of its maximal monotonicity. The example was developed with assistance from GPT-6 Astra. The purpose is to simplify and explain the construction, not to claim an independent counterexample mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13906",
  "author_total": 1,
  "authors": [
    {
      "name": "Radu Ioan Bot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vfddkype6pz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13906",
  "fulltext_url": null,
  "id": "4vfddkype6pz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13906",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7213363456",
  "pdf_url": "https://arxiv.org/pdf/2609.13906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vfddkype6pz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of Rockafellar's Sum Conjecture via an Explicit Non-(FPV) Operator",
  "title_text": "Failure of Rockafellar's Sum Conjecture via an Explicit Non-(FPV) Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4vfddkype6pz5",
  "venue": "arXiv",
  "versions": []
}