{
  "abstract": "We investigate the distance from the centre of an even integer to its nearest Goldbach representation, emphasizing the guaranteed-reset progression $N\\equiv10\\pmod{60}$. Candidate representations occur at the lattice sites $N/2\\pm6j$, and the first successful site defines a first-arrival process in the normalized imbalance interval. For arbitrary finite families of candidate sites we prove an exact Chinese-remainder-theorem density formula for surviving local congruence classes. The associated two-site multiplier is explicitly repulsive in the generic case and attractive when $i\\equiv\\pm j\\pmod\\ell$. A four-site selection gives an exact joint non-occurrence theorem modulo $7$. Computations over $483{,}333$ even targets in $[10^6,3\\cdot10^7]$ compare sieve-predicted pair correlations with actual prime pairs and examine the void probability using the first three factorial cumulants. We formulate and prove a conditional moment-to-Poisson theorem that isolates the stronger, presently unavailable, high-order prime-tuple estimates required for an exponential first-arrival law. All finite residue-count identities are unconditional; numerical fits, heuristic Euler products, and asymptotic conjectures are labeled separately.",
  "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/54bd5fd8r2235.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23463921",
  "fulltext_url": null,
  "id": "54bd5fd8r2235",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23463921",
  "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/23463921/files/goldbach_first_arrival.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54bd5fd8r2235.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:46Z",
      "native_id": "23463921",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23463921"
    }
  ],
  "subjects": [],
  "title": "Joint Local Sieves and First-Arrival Dynamics of Goldbach Imbalances: Exact Modular Correlations, Void Probabilities, Factorial Cumulants and a Conditional Poisson Law",
  "title_text": "Joint Local Sieves and First-Arrival Dynamics of Goldbach Imbalances: Exact Modular Correlations, Void Probabilities, Factorial Cumulants and a Conditional Poisson Law",
  "type": "preprint",
  "updated_at": "2026-11-02T12:20:46Z",
  "url": "https://research.draconitic.com/paper/54bd5fd8r2235",
  "venue": "Zenodo",
  "versions": []
}