{
  "abstract": "GST v1.19 recorded that the set C_2 used by the class C evaluation has 59 members, a value read from the evaluation output. This manuscript explains where that number comes from and checks the explanation by machine. Let z_t be the 12-pair cut of v1.19 (Y_9 without 4>1), and H the set of sub-relations w of z_t with the same reflexive transitive closure as z_t. A replacement lemma reduces membership in H to replacement paths; for z_t this gives a necessary and sufficient condition in four independent groups of pairs (five pairs always kept; at least one of 1>0, 1>3; 0>4, or both 0>3 and 3>4; 5>0 and 5>2 free), so |H| = 1 x 3 x 5 x 4 = 60 and |H - {z_t}| = 59. Every member of H is persistent and not closed: having the closure of z_t, it keeps the mutual reachability of 0 and 2, and it keeps the reachability of 2 from 1 while the pair 1>2 is absent, so it is not closed. A pre-registered finite check, run once against the fixed cone_lib code on all 4096 subsets of z_t, found the code's closure test and the stated condition in agreement on every subset, and the persistence and non-closedness properties on all 60 members, with its controls behaving as registered. Under the cited lemma D2 and the C-cone reservation kept from v1.19, H - {z_t} is C_2; by the code definitions, the same 59 cuts have letter 000 relative to z_t and 100 relative to Y_9, the only change being the new reachability from S = {0, 2, 3, 4} into node 1 through 4>1. The member list reported by the class C evaluation was not compared, and nothing is claimed about acceptance at a root or about why the stored answer was chosen.",
  "abstract_shown": true,
  "affiliations": [
    "SD Lab LLC"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Koji Okino",
      "orcid": "0009-0003-9273-9813"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fy1ymhskz779g.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23438525",
  "fulltext_url": null,
  "id": "fy1ymhskz779g",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23438525",
  "language": "eng",
  "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/23438525/files/GST_v1.20_paper.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fy1ymhskz779g.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:16Z",
      "native_id": "23438525",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23438525"
    }
  ],
  "subjects": [],
  "title": "Generative Structural Theory v1.20 — Where the 59 Cuts Come From: The Closure-Preserving Sub-relations of z_t, a Finite Machine Check of Their Characterisation, and a Conditional Connection with C_2",
  "title_text": "Generative Structural Theory v1.20 — Where the 59 Cuts Come From: The Closure-Preserving Sub-relations of z_t, a Finite Machine Check of Their Characterisation, and a Conditional Connection with C_2",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:16Z",
  "url": "https://research.draconitic.com/paper/fy1ymhskz779g",
  "venue": "Zenodo",
  "versions": []
}