{
  "abstract": "For each even integer $2n$, let $S(n)=\\{p\\in\\PP:2n-p\\in\\PP\\}$ be the set of prime summands of its Goldbach representations, and let $I_k(n)=S(n)\\cap S(n-k)$. These intersections encode prime pairs of every even separation. We develop exact correspondences, a zero-or-many theorem for nonempty intersection rows, consequences of finite and infinite fixed-gap prime-pair classes, and counterexamples showing why gap recurrence and neighboring-row overlaps alone cannot prove Goldbach. We then study crossed intersections $B_h(n)$ and prove that they are precisely fixed-gap autocorrelations of $S(n)$. On the residue class $n\\equiv1\\pmod3$ where the summand 3 is unavailable, modulo-3 selection restricts nonexceptional crossed bridges to gaps divisible by six. For gaps $6,12,18$ we derive their four-prime singular series and local modulation modulo 5 and 7, prove exact overlap exclusions and a pair-count conservation law, and provide reproducible computations through $n\\le10^6$. There are 258,814 tested extinction indices and no simultaneous zero of the three crossed-bridge counts. The numerical and heuristic observations are explicitly separated from theorems: universal short-gap rescue, the twin-prime conjecture, and the binary Goldbach conjecture remain unproved.",
  "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/8hx3yy8gkhrvw.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23463891",
  "fulltext_url": null,
  "id": "8hx3yy8gkhrvw",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23463891",
  "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/23463891/files/goldbach_intersections.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hx3yy8gkhrvw.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:46Z",
      "native_id": "23463891",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23463891"
    }
  ],
  "subjects": [],
  "title": "Goldbach Intersection Geometry and Prime-Pair Correlations: Exact Identities, Crossed Bridges, Modular Selection, Singular Series, and Computational Evidence",
  "title_text": "Goldbach Intersection Geometry and Prime-Pair Correlations: Exact Identities, Crossed Bridges, Modular Selection, Singular Series, and Computational Evidence",
  "type": "preprint",
  "updated_at": "2026-11-02T12:20:46Z",
  "url": "https://research.draconitic.com/paper/8hx3yy8gkhrvw",
  "venue": "Zenodo",
  "versions": []
}