{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RBY4D3XOUVDC4PDZTBE3T2IGQT","short_pith_number":"pith:RBY4D3XO","schema_version":"1.0","canonical_sha256":"8871c1eeeea5462e3c799849b9e90684e8baa819d56b0942b2bd54ebfbe15fb5","source":{"kind":"arxiv","id":"1904.03585","version":5},"attestation_state":"computed","paper":{"title":"Lie, associative and commutative quasi-isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Daniel Robert-Nicoud, Dan Petersen, Felix Wierstra, Ricardo Campos","submitted_at":"2019-04-07T05:22:45Z","abstract_excerpt":"Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational homotopy theory, showing that the rational homotopy type of a space is determined by its associative dg algebra of rational cochains. We also show a Koszul dual statement, under an additional completeness hypothesis: two homotopy complete dg Lie algebras whose universal enveloping algebras are quasi-isomorphic as associative dg algebras must themselves be quasi-is"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.03585","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-07T05:22:45Z","cross_cats_sorted":["math.AT","math.KT","math.QA","math.RT"],"title_canon_sha256":"330b091e5c6749c01bd0ed36eed25523ce9c546d8d7d4cfc4d7c59de3fbc8c05","abstract_canon_sha256":"7f60a19365093a02698b12c47a48e454c3e57cf4ded1585a209b364a8a2d2acd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:30:49.868778Z","signature_b64":"vvVO61P4cr2P3+uSLZGHdzV9+ShBpOC7r6LsQRpHyarm3v7TWk1FSqYsEJmeYx6yzaZUO5zQS2txrN97QyC9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8871c1eeeea5462e3c799849b9e90684e8baa819d56b0942b2bd54ebfbe15fb5","last_reissued_at":"2026-07-05T10:30:49.868235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:30:49.868235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie, associative and commutative quasi-isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Daniel Robert-Nicoud, Dan Petersen, Felix Wierstra, Ricardo Campos","submitted_at":"2019-04-07T05:22:45Z","abstract_excerpt":"Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational homotopy theory, showing that the rational homotopy type of a space is determined by its associative dg algebra of rational cochains. We also show a Koszul dual statement, under an additional completeness hypothesis: two homotopy complete dg Lie algebras whose universal enveloping algebras are quasi-isomorphic as associative dg algebras must themselves be quasi-is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03585","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.03585/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.03585","created_at":"2026-07-05T10:30:49.868291+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03585v5","created_at":"2026-07-05T10:30:49.868291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03585","created_at":"2026-07-05T10:30:49.868291+00:00"},{"alias_kind":"pith_short_12","alias_value":"RBY4D3XOUVDC","created_at":"2026-07-05T10:30:49.868291+00:00"},{"alias_kind":"pith_short_16","alias_value":"RBY4D3XOUVDC4PDZ","created_at":"2026-07-05T10:30:49.868291+00:00"},{"alias_kind":"pith_short_8","alias_value":"RBY4D3XO","created_at":"2026-07-05T10:30:49.868291+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT","json":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT.json","graph_json":"https://pith.science/api/pith-number/RBY4D3XOUVDC4PDZTBE3T2IGQT/graph.json","events_json":"https://pith.science/api/pith-number/RBY4D3XOUVDC4PDZTBE3T2IGQT/events.json","paper":"https://pith.science/paper/RBY4D3XO"},"agent_actions":{"view_html":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT","download_json":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT.json","view_paper":"https://pith.science/paper/RBY4D3XO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03585&json=true","fetch_graph":"https://pith.science/api/pith-number/RBY4D3XOUVDC4PDZTBE3T2IGQT/graph.json","fetch_events":"https://pith.science/api/pith-number/RBY4D3XOUVDC4PDZTBE3T2IGQT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT/action/storage_attestation","attest_author":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT/action/author_attestation","sign_citation":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT/action/citation_signature","submit_replication":"https://pith.science/pith/RBY4D3XOUVDC4PDZTBE3T2IGQT/action/replication_record"}},"created_at":"2026-07-05T10:30:49.868291+00:00","updated_at":"2026-07-05T10:30:49.868291+00:00"}