{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "runge-numerical-differential-equations-1895",
    "title": "Runge: Ueber die numerische Auflösung von Differentialgleichungen",
    "summary": "Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.",
    "boundary": "The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.",
    "area": "Numerical and computational mathematics",
    "year": 1895,
    "lane": "HUMAN",
    "result": "ALGORITHM",
    "package_id": "runge-numerical-differential-equations-1895",
    "target": {
      "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
      "version": 1,
      "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
    },
    "humans": [
      "Carl Runge"
    ],
    "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": "springer-runge-ode-1895",
        "title": "Springer DOI record for Runge numerical ODE paper",
        "url": "https://doi.org/10.1007/BF01446807"
      },
      {
        "id": "crossref-runge-ode-1895",
        "title": "Crossref record for Runge numerical ODE paper",
        "url": "https://api.crossref.org/works/10.1007%2FBF01446807"
      }
    ],
    "geography": {
      "country_codes": [
        "DE"
      ],
      "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://www.deutsche-biographie.de/118803476.html",
      "target": {
        "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
        "version": 1,
        "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
      },
      "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION",
      "reviewed_on": "2026-09-26",
      "nationality_inferred": false,
      "sources": [
        {
          "title": "Attribution source",
          "url": "https://www.deutsche-biographie.de/118803476.html"
        }
      ],
      "coverage_status": "COMPLETE",
      "country_labels": {
        "DE": "Germany"
      }
    },
    "points": "120000",
    "published_grade": {
      "id": "runge-numerical-differential-equations-1895",
      "entry_id": "runge-numerical-differential-equations-1895",
      "band": "A",
      "modifier": "-",
      "target": {
        "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
        "version": 1,
        "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
      },
      "what_changed": "Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.",
      "scope": "The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.",
      "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:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
        "version": 1,
        "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
      },
      "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": "Carl Runge",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "Springer DOI record for Runge numerical ODE paper",
            "url": "https://doi.org/10.1007/BF01446807"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "Springer DOI record for Runge numerical ODE paper",
            "url": "https://doi.org/10.1007/BF01446807"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "Crossref record for Runge numerical ODE paper",
            "url": "https://api.crossref.org/works/10.1007%2FBF01446807"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.",
        "domain": "Numerical and computational mathematics"
      },
      "sources": [
        {
          "citation": "Springer DOI record for Runge numerical ODE paper",
          "url": "https://doi.org/10.1007/BF01446807"
        },
        {
          "citation": "Crossref record for Runge numerical ODE paper",
          "url": "https://api.crossref.org/works/10.1007%2FBF01446807"
        }
      ],
      "statement": "# Runge: Ueber die numerische Auflösung von Differentialgleichungen\n\nDeveloped multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.\n\n## Scientific scope\n\nThe record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.\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\nCarl Runge\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- [Springer DOI record for Runge numerical ODE paper](https://doi.org/10.1007/BF01446807)\n- [Crossref record for Runge numerical ODE paper](https://api.crossref.org/works/10.1007%2FBF01446807)\n",
      "summary": "Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.",
      "title": "Runge: Ueber die numerische Auflösung von Differentialgleichungen"
    },
    "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
      "version": 1,
      "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:25f5b8ffd2b50879625e9412638e8435897ecc5270b4d5150b845c3323ebf756"
  },
  "target": {
    "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
    "version": 1,
    "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "runge-numerical-differential-equations-1895",
    "entry_id": "runge-numerical-differential-equations-1895",
    "revision": 1,
    "title": "Runge: Ueber die numerische Auflösung von Differentialgleichungen",
    "context": "Numerical and computational mathematics",
    "track": "ALGORITHM",
    "band": "A",
    "modifier": "-",
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-09-25",
    "evidence_cutoff": "2026-09-25",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.",
    "scope": "The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.",
    "evidence_summary": "The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.",
    "references": [
      {
        "title": "Springer DOI record for Runge numerical ODE paper",
        "url": "https://doi.org/10.1007/BF01446807",
        "locator": "Source for the stated contribution; scientific claims remain bounded to the linked work."
      },
      {
        "title": "Crossref record for Runge numerical ODE paper",
        "url": "https://api.crossref.org/works/10.1007%2FBF01446807",
        "locator": "Source for the stated contribution; scientific claims remain bounded to the linked work."
      }
    ],
    "roles": [
      {
        "who": "Carl Runge",
        "credit": "SCIENCE",
        "did": "Named source author of the scoped work; individual effort shares are not measured."
      }
    ],
    "target": {
      "record_id": "urn:uuid:7ab3fa34-4ce6-4d6e-a1ad-1784ee415ed3",
      "version": 1,
      "content_hash": "sha256:a49182c63a08fd3c76bdd8750d172df7548b5b0a4acc2056d8cba5e5a37fa72f"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "120000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}