{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
    "title": "Kruskal: a global map of the extended Schwarzschild spacetime",
    "summary": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.\n\nA coordinate system can show only part of a spacetime, much as one map can omit a region of the Earth. The original Schwarzschild coordinates break down at a horizon; Finkelstein had continued through one horizon branch. Kruskal supplied a particularly clear global map: both horizon branches and a second exterior region fit into one regular representation. Radial light rays become straight diagonal lines, making the allowed causal connections easy to follow. The horizon is regular, but the center remains a genuine curvature singularity. The bridge pictured in the paper does not provide a traversable shortcut or a model of an actual collapsing star. Earlier extension work is acknowledged in the original, and Szekeres independently obtained the same extension. This record credits Kruskal’s explicit representation and scoped maximality argument, not every later black-hole result.",
    "boundary": "The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.",
    "area": "Physics",
    "topic": "Horizons and global spacetime geometry",
    "year": 1960,
    "lane": "HUMAN",
    "result": "THEORY",
    "package_id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
    "target": {
      "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
      "version": 1,
      "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
    },
    "humans": [
      "M. D. Kruskal"
    ],
    "authors_complete": true,
    "human_role_note": "Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.",
    "agents": [],
    "related": [
      "schwarzschild-static-spherical-vacuum-exact-solution-1916",
      "finkelstein-schwarzschild-horizon-causal-extension-1958"
    ],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "wrs24-kruskal-explicit-maximal-schwarzschild-extension-1960-original",
        "title": "M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745",
        "url": "https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf"
      },
      {
        "id": "wrs24-kruskal-explicit-maximal-schwarzschild-extension-1960-original-publisher",
        "title": "APS1960originalbibliographicidentity/byline",
        "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743"
      },
      {
        "id": "wrs24-kruskal-explicit-maximal-schwarzschild-extension-1960-original-modern",
        "title": "Cederbaum and Wolff2024 selected introduction andgeneralizedextensionconstruction",
        "url": "https://link.springer.com/article/10.1007/s11005-024-01779-y"
      }
    ],
    "points": "240000",
    "published_grade": {
      "id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
      "entry_id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
      "band": "A",
      "modifier": null,
      "target": {
        "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
        "version": 1,
        "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
      },
      "what_changed": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.",
      "scope": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity. The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.",
      "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:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
        "version": 1,
        "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-10-03T00:00:00Z",
    "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. D. Kruskal",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745",
            "url": "https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745",
            "url": "https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "APS1960originalbibliographicidentity/byline",
            "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-2",
          "kind": "source_reference",
          "source": {
            "citation": "Cederbaum and Wolff2024 selected introduction andgeneralizedextensionconstruction",
            "url": "https://link.springer.com/article/10.1007/s11005-024-01779-y"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.",
        "domain": "Physics"
      },
      "sources": [
        {
          "citation": "M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745",
          "url": "https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf"
        },
        {
          "citation": "APS1960originalbibliographicidentity/byline",
          "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743"
        },
        {
          "citation": "Cederbaum and Wolff2024 selected introduction andgeneralizedextensionconstruction",
          "url": "https://link.springer.com/article/10.1007/s11005-024-01779-y"
        }
      ],
      "statement": "# Kruskal: a global map of the extended Schwarzschild spacetime\n\nKruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.\n\nA coordinate system can show only part of a spacetime, much as one map can omit a region of the Earth. The original Schwarzschild coordinates break down at a horizon; Finkelstein had continued through one horizon branch. Kruskal supplied a particularly clear global map: both horizon branches and a second exterior region fit into one regular representation. Radial light rays become straight diagonal lines, making the allowed causal connections easy to follow. The horizon is regular, but the center remains a genuine curvature singularity. The bridge pictured in the paper does not provide a traversable shortcut or a model of an actual collapsing star. Earlier extension work is acknowledged in the original, and Szekeres independently obtained the same extension. This record credits Kruskal’s explicit representation and scoped maximality argument, not every later black-hole result.\n\n## Scientific scope\n\nThe extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.\n\n## People and systems\n\nM. D. Kruskal\n\n\n\n## Original sources\n\n- [M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745](https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf)\n- [APS1960originalbibliographicidentity/byline](https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743)\n- [Cederbaum and Wolff2024 selected introduction andgeneralizedextensionconstruction](https://link.springer.com/article/10.1007/s11005-024-01779-y)\n",
      "summary": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.\n\nA coordinate system can show only part of a spacetime, much as one map can omit a region of the Earth. The original Schwarzschild coordinates break down at a horizon; Finkelstein had continued through one horizon branch. Kruskal supplied a particularly clear global map: both horizon branches and a second exterior region fit into one regular representation. Radial light rays become straight diagonal lines, making the allowed causal connections easy to follow. The horizon is regular, but the center remains a genuine curvature singularity. The bridge pictured in the paper does not provide a traversable shortcut or a model of an actual collapsing star. Earlier extension work is acknowledged in the original, and Szekeres independently obtained the same extension. This record credits Kruskal’s explicit representation and scoped maximality argument, not every later black-hole result.",
      "title": "Kruskal: a global map of the extended Schwarzschild spacetime"
    },
    "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
      "version": 1,
      "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:261b7a98a191185e3c66c7610ed0f4572a6f1004c3953cbb7a6d3a9ed7884a17"
  },
  "target": {
    "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
    "version": 1,
    "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
    "entry_id": "kruskal-explicit-maximal-schwarzschild-extension-1960",
    "revision": 1,
    "title": "Kruskal: a global map of the extended Schwarzschild spacetime",
    "context": "Physics",
    "track": "Physics",
    "band": "A",
    "modifier": null,
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-10-04",
    "evidence_cutoff": "2026-10-04",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.",
    "scope": "Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity. The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.",
    "evidence_summary": "Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.",
    "references": [
      {
        "title": "M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960 original 1743-1745",
        "url": "https://lilith.fisica.ufmg.br/dsoares/extn/brcs/kruskal-1960.pdf",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      },
      {
        "title": "APS 1960 originalbibliographicidentity/byline",
        "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.119.1743",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      },
      {
        "title": "Cederbaum and Wolff 2024 selected introduction andgeneralizedextensionconstruction",
        "url": "https://link.springer.com/article/10.1007/s11005-024-01779-y",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      }
    ],
    "roles": [
      {
        "who": "M. D. Kruskal",
        "did": "Original source-listed scientific author of this scoped work; byline does not determine effort fractions.",
        "credit": "SCIENCE"
      }
    ],
    "target": {
      "record_id": "urn:uuid:9a4bed9c-74be-4ddd-a5ab-077e39dd41c8",
      "version": 1,
      "content_hash": "sha256:8960dc3932d96062feeb9358c16eead0ac0b406506b280e83f9d921502647ade"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "240000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}