{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "kepler-formal", "title": "Flyspeck: formalizing the Kepler conjecture", "summary": "Formalizes the proof of the densest three-dimensional sphere packing using HOL Light and Isabelle.", "boundary": "The 22-person byline of arXiv:1501.02155v1 is recorded. HOL Light and Isabelle formalization is distinct from modern generative AI. These are paper authors, not an assertion that all project participants or individual formalization roles have been exhaustively reconstructed.", "area": "Discrete geometry", "topic": "Mathematics & logic", "year": 2015, "lane": "HUMAN", "result": "FORMALIZATION", "package_id": "kepler-formal", "target": { "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "content_hash": "sha256:36c97191ae63584d27703657a5b33bf0bc3c38a8b9f713faca78e3b9ec112c0d" }, "humans": [ "Thomas Hales", "Mark Adams", "Gertrud Bauer", "Dat Tat Dang", "John Harrison", "Truong Le Hoang", "Cezary Kaliszyk", "Victor Magron", "Sean McLaughlin", "Thang Tat Nguyen", "Truong Quang Nguyen", "Tobias Nipkow", "Steven Obua", "Joseph Pleso", "Jason Rute", "Alexey Solovyev", "An Hoai Thi Ta", "Trung Nam Tran", "Diep Thi Trieu", "Josef Urban", "Ky Khac Vu", "Roland Zumkeller" ], "human_identities": [ { "author_position": 0, "source_name": "Thomas Hales", "person_id": "wrs-person-4c80ea54a555b79ec0396d1d", "display_name": "Thomas C. 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the specified HOL Light and Isabelle formalization.", "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:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "content_hash": "sha256:36c97191ae63584d27703657a5b33bf0bc3c38a8b9f713faca78e3b9ec112c0d" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": { "content_hash": "sha256:b0fd0ebc273579acacf549dd62bf9ee865e54f367949d87478893b3e80b936b7", "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 1 }, "published_at": "2026-09-12T00:00:00Z", "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": "Thomas Hales", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Mark Adams", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Gertrud Bauer", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Dat Tat Dang", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "John Harrison", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Truong Le Hoang", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Cezary Kaliszyk", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Victor Magron", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Sean McLaughlin", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Thang Tat Nguyen", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Truong Quang Nguyen", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Tobias Nipkow", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Steven Obua", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Joseph Pleso", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Jason Rute", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Alexey Solovyev", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "An Hoai Thi Ta", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Trung Nam Tran", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Diep Thi Trieu", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Josef Urban", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Ky Khac Vu", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Roland Zumkeller", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formalizer" ], "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "The 22-person byline of arXiv:1501.02155v1 is recorded. HOL Light and Isabelle formalization is distinct from modern generative AI. These are paper authors, not an assertion that all project participants or individual formalization roles have been exhaustively reconstructed.", "domain": "离散几何" }, "sources": [ { "citation": "Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)", "url": "https://arxiv.org/abs/1501.02155" } ], "statement": "# Flyspeck: formalizing the Kepler conjecture\n\nFormalizes the proof of the densest three-dimensional sphere packing using HOL Light and Isabelle.\n\n## Scientific scope\n\nThe 22-person byline of arXiv:1501.02155v1 is recorded. HOL Light and Isabelle formalization is distinct from modern generative AI. These are paper authors, not an assertion that all project participants or individual formalization roles have been exhaustively reconstructed.\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\nThomas Hales; Mark Adams; Gertrud Bauer; Dat Tat Dang; John Harrison; Truong Le Hoang; Cezary Kaliszyk; Victor Magron; Sean McLaughlin; Thang Tat Nguyen; Truong Quang Nguyen; Tobias Nipkow; Steven Obua; Joseph Pleso; Jason Rute; Alexey Solovyev; An Hoai Thi Ta; Trung Nam Tran; Diep Thi Trieu; Josef Urban; Ky Khac Vu; Roland Zumkeller\n\nListed source contributors; individual labor shares are not measured\n\n\n\n## Original sources\n\n- [Hales et al., A formal proof of the Kepler conjecture (2015; published account 2017)](https://arxiv.org/abs/1501.02155)\n", "summary": "Formalizes the proof of the densest three-dimensional sphere packing using HOL Light and Isabelle.", "title": "Flyspeck: formalizing the Kepler conjecture" }, "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "source_ref": { "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "content_hash": "sha256:36c97191ae63584d27703657a5b33bf0bc3c38a8b9f713faca78e3b9ec112c0d" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:4673435f6846172ee4961230610f580728f5492d796974b6cee4463faa194158" }, "target": { "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "content_hash": "sha256:36c97191ae63584d27703657a5b33bf0bc3c38a8b9f713faca78e3b9ec112c0d" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "kepler-formal", "entry_id": "kepler-formal", "revision": 1, "title": "A complex packing proof becomes formally checkable", "context": "Large mathematical proof formalization", "track": "Formal verification", "band": "A", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-09-13", "evidence_cutoff": "2026-09-13", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "A large proof combining mathematical arguments and computation was translated into a proof-assistant verification workflow.", "scope": "Congruent sphere packing in Euclidean three-space; the specified HOL Light and Isabelle formalization.", "evidence_summary": "The project’s published account describes the completed proof and its verification components. Its earlier proof-review history helps explain what the formalization added.", "references": [ { "title": "Hales et al.: A formal proof of the Kepler conjecture", "url": "https://arxiv.org/html/1501.02155v1", "locator": "Sections 1, 2, 3 and 10; project components and trust boundary" } ], "roles": [ { "who": "Hales and the 22-person paper byline", "credit": "VERIFICATION", "did": "The formalization project; complete retained byline remains in the linked record." }, { "who": "Ferguson and Hales", "credit": "SCIENCE", "did": "Earlier Kepler proof contribution; it is not counted again as a new discovery here." }, { "who": "HOL Light and Isabelle", "credit": "INFRASTRUCTURE", "did": "Proof-assistant tools, not modern generative-AI authors." } ], "target": { "record_id": "urn:uuid:452b9fcf-8d58-4deb-ac68-91dc425533a1", "version": 2, "content_hash": "sha256:36c97191ae63584d27703657a5b33bf0bc3c38a8b9f713faca78e3b9ec112c0d" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "40000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }