{
  "abstract": "We study a deletion rule for strictly convex quadratic minimization on a simplex: compute the affine minimizer on the current face, permanently remove a most-negative coordinate, and repeat. Correctness is required for every linear term and every resolution of ties. We characterize first-step safety by a finite maximum principle for the constrained inverse, and correctness from every initial face by principal-inverse row inequalities. Correctness from the full simplex is a different property. The two properties coincide with at most four coordinates, but an explicit rational five-coordinate example separates them. An exact reachability condition explains the separation: boundary equalities in the constrained inverse restrict the tasks that can be entered on a facet. Away from these equalities, full-start and hereditary correctness coincide. We also determine the recognition complexity. First-step safety is decidable in polynomial bit time, by combining classical strict $n$-step-vector recognition with diagonal regularization. In contrast, full-start and hereditary correctness are coNP-complete, even on a reduction family with strict column diagonal maxima on every face. The proofs include the non-strict boundary and all affine anchors; explicit rational certificates for the finite examples are given in the text.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33908",
  "author_total": 1,
  "authors": [
    {
      "name": "Arseny Kosachev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3h77nzsfwswe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33908",
  "fulltext_url": null,
  "id": "f3h77nzsfwswe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33908",
  "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.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223880576",
  "pdf_url": "https://arxiv.org/pdf/2610.33908",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3h77nzsfwswe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33908",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33908"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Minimum-coordinate elimination on a simplex: polynomial first-step safety and coNP-complete correctness",
  "title_text": "Minimum-coordinate elimination on a simplex: polynomial first-step safety and coNP-complete correctness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/f3h77nzsfwswe",
  "venue": "arXiv",
  "versions": []
}