{
  "abstract": "This methodological preprint develops explicit interfaces between finite evidence and mathematical proof for FDCL models. Topics include geometric growth versus dimension, mass-aware residual bounds, exact rational acceptance, inertia transcripts, corrected outputs, variational means, and observable finite-state tail budgets. Version 1.2 adds transfer and application interfaces, including positive-pencil and definite-subspace certificates, and incorporates strengthened comparisons with prior work. The public package contains the current manuscript and LaTeX source, exact checkers, finite witnesses and reports, the pinned Part II mean-tail proof companion and Part VII source dependency, and lean inputs from the two non-backtracking applications. The application PDFs and semantic source are the current address-free v1.0 editions. Finite replay certifies specified finite statements; native constructor identities and imported all-level premises remain separately identified. Series and release: FDCL Part IX, Version 1.2, 15 October 2026; 56 pages and 39 references. This is a new version of the existing Part IX concept record. The two uploaded files are the public manuscript PDF and complete source/reproduction ZIP. SHA256SUMS.txt inside the ZIP covers the current distribution. The original mathematical statements, proofs, verifier code and stored arithmetic inputs were preserved during public packaging. The applications' historical method audits remain pinned to Part IX v1.1. Verification scope: the nine standard-library core commands, optional NumPy native replay and selected alpha mutation controls were rerun successfully from the public package. Stored finite certificate acceptance is distinguished from imported all-level proofs and general software soundness. Previous large numerical discovery campaigns were not rerun by this packaging step. AI assistance and author responsibility: OpenAI ChatGPT and Codex and Anthropic Claude were used substantively in proof strategies, candidate arguments and counterexamples, verification code, data analysis, literature comparisons, and English drafting and revision. Bin Seol directed the research and experiments, managed data and evolving definitions, organized repeated cross-domain stress tests, and selected and revised the final claims. He is the sole human author and takes responsibility for the content, source attribution and reported results. This research received no external funding.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Bin Seol",
      "orcid": "0009-0006-9530-4497"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ghsr1w87702p.bib",
  "cited_by": 9,
  "doi": "10.5281/zenodo.23227343",
  "fulltext_url": null,
  "id": "5ghsr1w87702p",
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  "landing_url": "https://doi.org/10.5281/zenodo.23227343",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220923524",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/5ghsr1w87702p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7220923524",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23227343"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Mathematical Dynamics and Fractals",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "FDCL Part IX: Proof Methods and Exact Certification for FDCL Models — From Finite Evidence to Uniform Theorems",
  "title_text": "FDCL Part IX: Proof Methods and Exact Certification for FDCL Models — From Finite Evidence to Uniform Theorems",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/5ghsr1w87702p",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}