{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "atiyah-singer-index-compact-manifolds-1963",
    "title": "Atiyah and Singer: the index of elliptic operators on compact manifolds",
    "summary": "Announced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.",
    "boundary": "The record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications remain separate.",
    "area": "Geometry",
    "year": 1963,
    "lane": "HUMAN",
    "result": "THEOREM",
    "package_id": "atiyah-singer-index-compact-manifolds-1963",
    "target": {
      "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
      "version": 1,
      "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
    },
    "humans": [
      "M. F. Atiyah",
      "I. M. Singer"
    ],
    "human_identities": [
      {
        "author_position": 0,
        "source_name": "M. F. Atiyah",
        "person_id": "wrs-person-6ec2b5e4a5291fcc133490a4",
        "display_name": "Michael Francis Atiyah",
        "status": "SOURCE_LINKED_IDENTITY",
        "sources": [
          {
            "title": "Attribution source",
            "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Atiyah/"
          },
          {
            "title": "Attribution source",
            "url": "https://www.ams.org/journals/notices/201910/rnoti-p1660.pdf"
          },
          {
            "title": "Attribution source",
            "url": "https://doi.org/10.1098/rsta.1983.0017"
          }
        ]
      }
    ],
    "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": "ams-atiyah-singer-index-1963",
        "title": "AMS copy of the Atiyah–Singer compact-manifold paper",
        "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf"
      },
      {
        "id": "crossref-atiyah-singer-index-1963",
        "title": "Crossref record for the Atiyah–Singer paper",
        "url": "https://api.crossref.org/works/10.1090%2FS0002-9904-1963-10957-X"
      }
    ],
    "geography": {
      "country_codes": [
        "GB",
        "US"
      ],
      "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://celebratio.org/Atiyah_MF/article/44/",
      "target": {
        "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
        "version": 1,
        "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
      },
      "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION",
      "reviewed_on": "2026-09-26",
      "nationality_inferred": false,
      "sources": [
        {
          "title": "Attribution source",
          "url": "https://celebratio.org/Atiyah_MF/article/44/"
        }
      ],
      "coverage_status": "COMPLETE",
      "country_labels": {
        "GB": "United Kingdom",
        "US": "United States"
      }
    },
    "points": "225000",
    "published_grade": {
      "id": "atiyah-singer-index-compact-manifolds-1963",
      "entry_id": "atiyah-singer-index-compact-manifolds-1963",
      "band": "A",
      "modifier": "+",
      "target": {
        "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
        "version": 1,
        "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
      },
      "what_changed": "Announced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.",
      "scope": "The record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications 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:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
        "version": 1,
        "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
      },
      "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": "M. F. Atiyah",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "prover"
          ],
          "source": {
            "citation": "AMS copy of the Atiyah–Singer compact-manifold paper",
            "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf"
          }
        },
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "I. M. Singer",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "prover"
          ],
          "source": {
            "citation": "AMS copy of the Atiyah–Singer compact-manifold paper",
            "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "AMS copy of the Atiyah–Singer compact-manifold paper",
            "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "Crossref record for the Atiyah–Singer paper",
            "url": "https://api.crossref.org/works/10.1090%2FS0002-9904-1963-10957-X"
          }
        }
      ],
      "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 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications remain separate.",
        "domain": "Geometry"
      },
      "sources": [
        {
          "citation": "AMS copy of the Atiyah–Singer compact-manifold paper",
          "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf"
        },
        {
          "citation": "Crossref record for the Atiyah–Singer paper",
          "url": "https://api.crossref.org/works/10.1090%2FS0002-9904-1963-10957-X"
        }
      ],
      "statement": "# Atiyah and Singer: the index of elliptic operators on compact manifolds\n\nAnnounced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.\n\n## Scientific scope\n\nThe record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications 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\nM. F. Atiyah; I. M. Singer\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- [AMS copy of the Atiyah–Singer compact-manifold paper](https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf)\n- [Crossref record for the Atiyah–Singer paper](https://api.crossref.org/works/10.1090%2FS0002-9904-1963-10957-X)\n",
      "summary": "Announced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.",
      "title": "Atiyah and Singer: the index of elliptic operators on compact manifolds"
    },
    "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
      "version": 1,
      "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:8ac5e6e70bae9dc04a5abce444051f4c5ebc26b0186986f2231e0e148125e427"
  },
  "target": {
    "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
    "version": 1,
    "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "atiyah-singer-index-compact-manifolds-1963",
    "entry_id": "atiyah-singer-index-compact-manifolds-1963",
    "revision": 1,
    "title": "Atiyah and Singer: the index of elliptic operators on compact manifolds",
    "context": "Geometry",
    "track": "THEOREM",
    "band": "A",
    "modifier": "+",
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-09-25",
    "evidence_cutoff": "2026-09-25",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Announced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.",
    "scope": "The record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications 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 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications remain separate.",
    "references": [
      {
        "title": "AMS copy of the Atiyah–Singer compact-manifold paper",
        "url": "https://www.ams.org/journals/bull/1963-69-03/S0002-9904-1963-10957-X/S0002-9904-1963-10957-X.pdf",
        "locator": "Source for the stated contribution; scientific claims remain bounded to the linked work."
      },
      {
        "title": "Crossref record for the Atiyah–Singer paper",
        "url": "https://api.crossref.org/works/10.1090%2FS0002-9904-1963-10957-X",
        "locator": "Source for the stated contribution; scientific claims remain bounded to the linked work."
      }
    ],
    "roles": [
      {
        "who": "M. F. Atiyah",
        "credit": "SCIENCE",
        "did": "Named source author of the scoped work; individual effort shares are not measured."
      },
      {
        "who": "I. M. Singer",
        "credit": "SCIENCE",
        "did": "Named source author of the scoped work; individual effort shares are not measured."
      }
    ],
    "target": {
      "record_id": "urn:uuid:746b7bc7-15d9-4075-a1f2-a5ea527b1a10",
      "version": 1,
      "content_hash": "sha256:c69fbbdc5b3cb3f4f6c6c8e01f9a16fc02e8a56859539be414e8b3de0ab50ad5"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "225000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}
