{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:36IM37J6R4ESR4X2VA2BPNOFB3","short_pith_number":"pith:36IM37J6","schema_version":"1.0","canonical_sha256":"df90cdfd3e8f0928f2faa83417b5c50eee270cafc18464ae763c84fba1f0e0eb","source":{"kind":"arxiv","id":"2212.11323","version":2},"attestation_state":"computed","paper":{"title":"Maurer-Cartan methods in deformation theory: the twisting procedure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT","math.RA"],"primary_cat":"math.QA","authors_text":"Bruno Vallette, Sergey Shadrin, Vladimir Dotsenko","submitted_at":"2022-12-21T19:37:26Z","abstract_excerpt":"This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer-Cartan element. The twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras is described by means of the action of the biggest deformation gauge group ever considered. We give a criterion on quadratic operads for the exi"},"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":"2212.11323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-12-21T19:37:26Z","cross_cats_sorted":["math.AT","math.CT","math.KT","math.RA"],"title_canon_sha256":"4701e283cd27cb63bf0a30ae8eb1fe249136c8bc586c27f31bad6e2abd2d75b4","abstract_canon_sha256":"01c5f1d2794f729300e791df9e6fc45e8f50b6785cfd5099eb254675b3c7e464"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:11:19.185089Z","signature_b64":"FLyVmiR6/9B8BgqE0krl1E7RxGdP7YKZMr/bNfpt6Q4W8nguIf3hRiG3mUXI3biGlHBcpxC5VDGtrS4qxxDBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df90cdfd3e8f0928f2faa83417b5c50eee270cafc18464ae763c84fba1f0e0eb","last_reissued_at":"2026-07-05T08:11:19.184732Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:11:19.184732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maurer-Cartan methods in deformation theory: the twisting procedure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT","math.RA"],"primary_cat":"math.QA","authors_text":"Bruno Vallette, Sergey Shadrin, Vladimir Dotsenko","submitted_at":"2022-12-21T19:37:26Z","abstract_excerpt":"This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer-Cartan element. The twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras is described by means of the action of the biggest deformation gauge group ever considered. We give a criterion on quadratic operads for the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11323","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.11323/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":"2212.11323","created_at":"2026-07-05T08:11:19.184789+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.11323v2","created_at":"2026-07-05T08:11:19.184789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11323","created_at":"2026-07-05T08:11:19.184789+00:00"},{"alias_kind":"pith_short_12","alias_value":"36IM37J6R4ES","created_at":"2026-07-05T08:11:19.184789+00:00"},{"alias_kind":"pith_short_16","alias_value":"36IM37J6R4ESR4X2","created_at":"2026-07-05T08:11:19.184789+00:00"},{"alias_kind":"pith_short_8","alias_value":"36IM37J6","created_at":"2026-07-05T08:11:19.184789+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/36IM37J6R4ESR4X2VA2BPNOFB3","json":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3.json","graph_json":"https://pith.science/api/pith-number/36IM37J6R4ESR4X2VA2BPNOFB3/graph.json","events_json":"https://pith.science/api/pith-number/36IM37J6R4ESR4X2VA2BPNOFB3/events.json","paper":"https://pith.science/paper/36IM37J6"},"agent_actions":{"view_html":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3","download_json":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3.json","view_paper":"https://pith.science/paper/36IM37J6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.11323&json=true","fetch_graph":"https://pith.science/api/pith-number/36IM37J6R4ESR4X2VA2BPNOFB3/graph.json","fetch_events":"https://pith.science/api/pith-number/36IM37J6R4ESR4X2VA2BPNOFB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3/action/storage_attestation","attest_author":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3/action/author_attestation","sign_citation":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3/action/citation_signature","submit_replication":"https://pith.science/pith/36IM37J6R4ESR4X2VA2BPNOFB3/action/replication_record"}},"created_at":"2026-07-05T08:11:19.184789+00:00","updated_at":"2026-07-05T08:11:19.184789+00:00"}