{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "liouville-transcendental-numbers-notes-1844",
    "title": "Liouville: 1844 notes establishing transcendental numbers",
    "summary": "Proved approximation bounds for algebraic irrational numbers and used them to exhibit broad classes of numbers that are neither rational nor algebraic.",
    "boundary": "The record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.",
    "area": "Number theory",
    "topic": "Mathematics",
    "year": 1844,
    "lane": "HUMAN",
    "result": "THEOREM",
    "package_id": "liouville-transcendental-numbers-notes-1844",
    "target": {
      "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
      "version": 1,
      "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
    },
    "humans": [
      "Joseph Liouville"
    ],
    "authors_complete": true,
    "human_role_note": "The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.",
    "agents": [],
    "related": [],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "academie-sciences-liouville-1844-issues",
        "title": "French Academy archive for 1844 Comptes rendus",
        "url": "https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/"
      },
      {
        "id": "bibnum-liouville-1844-analysis",
        "title": "BibNum scholarly analysis and translation of Liouville 1844",
        "url": "https://www.bibnum.education.fr/sites/default/files/Liouville-analyse-english.pdf"
      }
    ],
    "geography": {
      "country_codes": [
        "FR"
      ],
      "location_basis": "Documented research locations or paper affiliations for this contribution. Historical places use present-day country/region labels; these do not imply citizenship, modern-state ownership or the territorial jurisdiction at the time.",
      "source_url": "https://mathshistory.st-andrews.ac.uk/Biographies/Liouville/",
      "target": {
        "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
        "version": 1,
        "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
      },
      "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION",
      "reviewed_on": "2026-09-26",
      "nationality_inferred": false,
      "sources": [
        {
          "title": "Attribution source",
          "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Liouville/"
        },
        {
          "title": "Attribution source",
          "url": "https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/"
        }
      ],
      "coverage_status": "COMPLETE",
      "country_labels": {
        "FR": "France"
      }
    },
    "points": "280000",
    "published_grade": {
      "id": "liouville-transcendental-numbers-notes-1844",
      "entry_id": "liouville-transcendental-numbers-notes-1844",
      "band": "S",
      "modifier": "-",
      "target": {
        "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
        "version": 1,
        "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
      },
      "what_changed": "Used rational-approximation bounds to prove existence of explicit transcendental-number classes.",
      "scope": "The record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.",
      "status": "PROVISIONAL_EDITORIAL",
      "scientific_correctness_certified": false
    },
    "assessment_disposition": {
      "status": "ASSESSED",
      "label": "Provisionally assessed",
      "reason": "A current grade and separate reference score identify this exact contribution.",
      "target": {
        "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
        "version": 1,
        "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-09-25T00:00:00Z",
    "publisher": {
      "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33",
      "role": "WRS_EDITORIAL_PUBLICATION"
    },
    "record": {
      "contributors": [
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "Joseph Liouville",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "prover"
          ],
          "source": {
            "citation": "French Academy archive for 1844 Comptes rendus",
            "url": "https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "French Academy archive for 1844 Comptes rendus",
            "url": "https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "BibNum scholarly analysis and translation of Liouville 1844",
            "url": "https://www.bibnum.education.fr/sites/default/files/Liouville-analyse-english.pdf"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.",
        "domain": "Number theory"
      },
      "sources": [
        {
          "citation": "French Academy archive for 1844 Comptes rendus",
          "url": "https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/"
        },
        {
          "citation": "BibNum scholarly analysis and translation of Liouville 1844",
          "url": "https://www.bibnum.education.fr/sites/default/files/Liouville-analyse-english.pdf"
        }
      ],
      "statement": "# Liouville: 1844 notes establishing transcendental numbers\n\nProved approximation bounds for algebraic irrational numbers and used them to exhibit broad classes of numbers that are neither rational nor algebraic.\n\n## Scientific scope\n\nThe record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nJoseph Liouville\n\nThe named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.\n\n\n\n## Original sources\n\n- [French Academy archive for 1844 Comptes rendus](https://comptes-rendus.academie-sciences.fr/page/browse-old-issues-1835-1996_en/)\n- [BibNum scholarly analysis and translation of Liouville 1844](https://www.bibnum.education.fr/sites/default/files/Liouville-analyse-english.pdf)\n",
      "summary": "Proved approximation bounds for algebraic irrational numbers and used them to exhibit broad classes of numbers that are neither rational nor algebraic.",
      "title": "Liouville: 1844 notes establishing transcendental numbers"
    },
    "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
      "version": 1,
      "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:22df29ce2ae1f19a82c9502abf5e2008ef2541dc7efa9159a9298eb5ddbd5b16"
  },
  "target": {
    "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
    "version": 1,
    "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "liouville-transcendental-numbers-notes-1844",
    "entry_id": "liouville-transcendental-numbers-notes-1844",
    "revision": 1,
    "title": "Liouville: 1844 notes establishing transcendental numbers",
    "context": "Number theory",
    "track": "THEOREM",
    "band": "S",
    "modifier": "-",
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-09-25",
    "evidence_cutoff": "2026-09-25",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Used rational-approximation bounds to prove existence of explicit transcendental-number classes.",
    "scope": "The record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.",
    "evidence_summary": "The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record treats Liouville's linked Comptes rendus notes of 13 and 20 May 1844 as one tightly bounded achievement. It does not absorb his 1851 synthesis, later named Liouville constants or subsequent transcendence theorems.",
    "references": [
      {
        "title": "Liouville: 1844 notes establishing transcendental numbers",
        "url": "https://www.bnf.fr/fr/hermite-et-les-mysteres-de-lexponentielle-bibliographie-fevrier-2022",
        "locator": "Source for the stated contribution; scientific claims remain bounded to the linked work."
      }
    ],
    "roles": [
      {
        "who": "Joseph Liouville",
        "credit": "SCIENCE",
        "did": "Named source author of the scoped work; individual effort shares are not measured."
      }
    ],
    "target": {
      "record_id": "urn:uuid:92121424-f9f0-44fc-ac69-6494f356f37d",
      "version": 1,
      "content_hash": "sha256:864cb9175bbf2be2d07f69c1e2129824e00d721fd93d8d3c8ca530a55706be19"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "280000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}