{
  "abstract": "We present a self-contained, machine-checked formalization in the Lean 4 theorem prover (Mathlib4) of the core algebraic-topological invariants underlying discrete metric filtrations in Relational Resolution Theory (TRR 3.0). Specifically, we formalize: (1) the monotonicity and downward closure of Vietoris-Rips metric filtration complexes over arbitrary types with decidable equality, (2) the ungraded simplicial chain module modeled via finitely supported functions, (3) the linearity and nilpotency (d^2 = 0) of the simplicial boundary operator, (4) the fundamental cycle inclusion (im d <= ker d), and (5) grading and subcomplex invariance. All ten theorems in the development are verified with zero unproven assumptions (sorryAx is absent) and depend solely on the standard axioms [propext, Classical.choice, Quot.sound].\n\nThe underlying algorithmic pipeline and machine-checked formalization for TRR 3.0 are strictly licensed under the GNU Affero General Public License v3.0 (AGPL-3.0). Source code repository: https://github.com/RW-101/TRR3-formalization-",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ronen Weinberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nxqah3hcmmz6.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23448711",
  "fulltext_url": null,
  "id": "6nxqah3hcmmz6",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23448711",
  "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/23448711/files/TRR3_Preprint.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nxqah3hcmmz6.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:16Z",
      "native_id": "23448711",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23448711"
    }
  ],
  "subjects": [],
  "title": "Machine-Checked Simplicial Chain Complexes over F_2 and Metric Filtration Invariants for Relational Resolution Theory in Lean 4⁠",
  "title_text": "Machine-Checked Simplicial Chain Complexes over F_2 and Metric Filtration Invariants for Relational Resolution Theory in Lean 4⁠",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:16Z",
  "url": "https://research.draconitic.com/paper/6nxqah3hcmmz6",
  "venue": "Zenodo",
  "versions": []
}