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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\nGrigori Perelman; Richard Hamilton; Henri Poincaré\n\nListed source contributors; individual labor shares are not measured\n\n\n\n## Original sources\n\n- [Clay Mathematics Institute: Millennium Prize Problems](https://www.claymath.org/millennium-problems/)\n- [CMI Poincaré: Solved](https://www.claymath.org/millennium/poincare-conjecture/)\n- [Perelman, The entropy formula for the Ricci flow and its geometric applications (2002)](https://arxiv.org/abs/math/0211159)\n", "summary": "The spherical characterization of closed, simply connected three-manifolds, as a consequence of geometrization work.", "title": "Poincaré conjecture and Perelman’s geometrization work" }, "record_id": "urn:uuid:e454d58e-2dec-460d-ada7-bf88956cff21", "version": 1, "source_ref": { "record_id": "urn:uuid:e454d58e-2dec-460d-ada7-bf88956cff21", "version": 1, "content_hash": "sha256:e869df3da3fdd6d7bb3a7a07f36d1f7efd291dcd476b9dd8ece2d203914a8089" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:5d363438f6381266d33e719b309dc522ba29af52d2ac339253d9dbb06fadd3a7" }, "target": { "record_id": "urn:uuid:e454d58e-2dec-460d-ada7-bf88956cff21", "version": 1, "content_hash": "sha256:e869df3da3fdd6d7bb3a7a07f36d1f7efd291dcd476b9dd8ece2d203914a8089" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "poincare", "entry_id": "poincare", "revision": 2, "title": "A structural answer for three-dimensional spaces", "context": "Three-dimensional topology", "track": "Mathematical discovery", "band": "S", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-12", "evidence_cutoff": "2026-10-12", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Three-dimensional spaces can be understood through a proved geometric decomposition, resolving the Poincaré conjecture along the way.", "scope": "The closed three-manifold setting of geometrization. This S placement belongs to three-dimensional topology; it is not a civilization-wide comparison with medicine or energy.", "evidence_summary": "CMI marks the problem solved and describes the broader geometrization result. The linked 2002 paper introduces central Ricci-flow tools; that one abstract alone is not the complete proof.", "references": [ { "title": "CMI: Poincaré conjecture", "url": "https://www.claymath.org/millennium/poincare-conjecture/", "locator": "Solved status; Overview and Advanced" }, { "title": "Perelman: entropy and Ricci flow", "url": "https://arxiv.org/abs/math/0211159v1", "locator": "Abstract and version identity" } ], "roles": [ { "who": "Grigori Perelman", "credit": "SCIENCE", "did": "Proof of geometrization and the resulting Poincaré conclusion." }, { "who": "Richard Hamilton", "credit": "SCIENCE", "did": "Pioneering Ricci-flow program, a distinct precursor contribution." }, { "who": "Henri Poincaré; William Thurston", "credit": "SCIENCE", "did": "The Poincaré problem and geometrization framework, respectively." } ], "target": { "record_id": "urn:uuid:e454d58e-2dec-460d-ada7-bf88956cff21", "version": 1, "content_hash": "sha256:e869df3da3fdd6d7bb3a7a07f36d1f7efd291dcd476b9dd8ece2d203914a8089" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "500000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }