{
  "abstract": "We study Goldbach representations about a moving pivot, distinguishing the loss of a\n\ndirect continuation from the loss of all representations. For pivots congruent to 1 modulo\n\n3, direct extinction has an exact primality criterion. Dirichlet’s theorem then supplies\n\ninfinitely many such pivots. We conjecture that each extinction is rescued by a twin pair\n\nand a prime pair at distance four, and show that this conjecture implies binary Goldbach\n\nand infinitely many twin primes. An equivalent four-prime convolution leads to a stronger\n\nresidue-specific conjecture. An odd-only Eratosthenes sieve and a complete fallback search\n\ntest every pivot through 109: among 284,220,751 residue-specific targets, no failure occurs,\n\nand no extinction pivot occurs in the other residue classes. A stricter right-hand orientation\n\nalready fails at 277. We give exact algorithms, finite counts, code, and the logical limits of\n\nthese observations; neither Goldbach nor the twin-prime conjecture is proved.",
  "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/esy35rm9as4ts.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23410422",
  "fulltext_url": null,
  "id": "esy35rm9as4ts",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23410422",
  "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/23410422/files/Goldbach_transitions%20(1).pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/esy35rm9as4ts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:23Z",
      "native_id": "23410422",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23410422"
    }
  ],
  "subjects": [],
  "title": "Goldbach Midpoint Transitions and Twin–Cousin Rescue: A Computational Study to One Billion",
  "title_text": "Goldbach Midpoint Transitions and Twin–Cousin Rescue: A Computational Study to One Billion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:19Z",
  "url": "https://research.draconitic.com/paper/esy35rm9as4ts",
  "venue": "Zenodo",
  "versions": []
}