{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6CZIGPFI3WE5FDK6J2EQEBT7PF","short_pith_number":"pith:6CZIGPFI","schema_version":"1.0","canonical_sha256":"f0b2833ca8dd89d28d5e4e8902067f795d9e97561cad7992e27e3f27e55f6bab","source":{"kind":"arxiv","id":"1204.4999","version":2},"attestation_state":"computed","paper":{"title":"Algebraic models of non-connected spaces and homotopy theory of $L_\\infty$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Urtzi Buijs","submitted_at":"2012-04-23T08:34:13Z","abstract_excerpt":"We develop a homotopy theory of $L_\\infty$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category. As a result, we obtain a general procedure to algebraically model the rational homotopy type of non-connected spaces."},"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":"1204.4999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-23T08:34:13Z","cross_cats_sorted":[],"title_canon_sha256":"3d9c0b765b1e978f03ac35b0273e35c1b821205a606260cc5f5d2494e9a2eed7","abstract_canon_sha256":"271a12b4d57f500802f1d8ffe8159e936787ab21b3f3c260431139317dd71ce3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:48.415587Z","signature_b64":"DCpMPO3BvpGx+jgP8r7ZmoE5GykYfmqn4p37nroGcse2u6sk/eK8K2qFZBrPMBxVW389tt1IkSyOTtZbxstLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0b2833ca8dd89d28d5e4e8902067f795d9e97561cad7992e27e3f27e55f6bab","last_reissued_at":"2026-05-18T03:34:48.414840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:48.414840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic models of non-connected spaces and homotopy theory of $L_\\infty$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Urtzi Buijs","submitted_at":"2012-04-23T08:34:13Z","abstract_excerpt":"We develop a homotopy theory of $L_\\infty$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category. As a result, we obtain a general procedure to algebraically model the rational homotopy type of non-connected spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4999","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1204.4999","created_at":"2026-05-18T03:34:48.414984+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.4999v2","created_at":"2026-05-18T03:34:48.414984+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4999","created_at":"2026-05-18T03:34:48.414984+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CZIGPFI3WE5","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CZIGPFI3WE5FDK6","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CZIGPFI","created_at":"2026-05-18T12:26:56.085431+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/6CZIGPFI3WE5FDK6J2EQEBT7PF","json":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF.json","graph_json":"https://pith.science/api/pith-number/6CZIGPFI3WE5FDK6J2EQEBT7PF/graph.json","events_json":"https://pith.science/api/pith-number/6CZIGPFI3WE5FDK6J2EQEBT7PF/events.json","paper":"https://pith.science/paper/6CZIGPFI"},"agent_actions":{"view_html":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF","download_json":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF.json","view_paper":"https://pith.science/paper/6CZIGPFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.4999&json=true","fetch_graph":"https://pith.science/api/pith-number/6CZIGPFI3WE5FDK6J2EQEBT7PF/graph.json","fetch_events":"https://pith.science/api/pith-number/6CZIGPFI3WE5FDK6J2EQEBT7PF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF/action/storage_attestation","attest_author":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF/action/author_attestation","sign_citation":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF/action/citation_signature","submit_replication":"https://pith.science/pith/6CZIGPFI3WE5FDK6J2EQEBT7PF/action/replication_record"}},"created_at":"2026-05-18T03:34:48.414984+00:00","updated_at":"2026-05-18T03:34:48.414984+00:00"}