{
  "abstract": "We investigate a proposed rescue mechanism for Goldbach representations at indices\n\n$n\\equiv1\\pmod3$ where the exceptional Goldbach summand $3$ is unavailable.\n\nThe proposed rescue uses a prime pair $(q,q+6)$ and a complementary prime $r$,\n\nso that $q+r=2n-4$ and $(q+6)+r=2n+2$. Writing $n=3t+1$ reduces the\n\nproblem to positivity of the discrete convolution\n\n$R(t)=\\sum_{a=1}^{t-1}f(a)f(a+1)f(t-a)$, where\n\n$f(a)=\\one_{\\PP}(6a-1)$. We give exact gcd identities, the associated\n\nsingular series and its uniform positivity, elementary rough-number bounds,\n\nfinite local-covering certificates, and infinite families of prescribed\n\nextinction and recovery. A conditional covariance criterion isolates the\n\nadditional additive information required to prove universal rescue.\n\nExact modular convolutions verify $R(t)>0$ for $2\\le t\\le10^6$.\n\nThe universal rescue assertion and the infinitude of sexy-prime pairs\n\nremain open; the note does not claim a solution of either problem.",
  "abstract_shown": true,
  "affiliations": [
    "Imperial College London"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Paul Alexander Bilokon",
      "orcid": "0000-0001-6846-6649"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g9ex4f5q79tt.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23463823",
  "fulltext_url": null,
  "id": "9g9ex4f5q79tt",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23463823",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23463823/files/sexy_prime_rescue.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g9ex4f5q79tt.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:47Z",
      "native_id": "23463823",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23463823"
    }
  ],
  "subjects": [],
  "title": "Sexy-Prime Bridges Across Goldbach Transitions: Exact Convolutions, Modular Extinction, Local Sieve Dynamics, and Conditional Covering Criteria",
  "title_text": "Sexy-Prime Bridges Across Goldbach Transitions: Exact Convolutions, Modular Extinction, Local Sieve Dynamics, and Conditional Covering Criteria",
  "type": "preprint",
  "updated_at": "2026-11-02T12:20:47Z",
  "url": "https://research.draconitic.com/paper/9g9ex4f5q79tt",
  "venue": "Zenodo",
  "versions": []
}