{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:STXVLWPVXLVJLJYV2EMDKDXTBS","short_pith_number":"pith:STXVLWPV","canonical_record":{"source":{"id":"1712.05619","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2017-12-15T11:15:08Z","cross_cats_sorted":[],"title_canon_sha256":"4215f3c9f4346d7559507a3b74279d056c6dfc2af8da260c12910da5ff39fe74","abstract_canon_sha256":"0ca86ea45a2e50117b90b2392f6a44f34b6b680f5d2b8dc42ef0d7775d90475c"},"schema_version":"1.0"},"canonical_sha256":"94ef55d9f5baea95a715d118350ef30cb4dd0706571a081c6980e243c1b8c620","source":{"kind":"arxiv","id":"1712.05619","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05619","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05619v3","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05619","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"STXVLWPVXLVJ","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_16","alias_value":"STXVLWPVXLVJLJYV","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_8","alias_value":"STXVLWPV","created_at":"2026-07-05T06:33:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:STXVLWPVXLVJLJYV2EMDKDXTBS","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05619","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2017-12-15T11:15:08Z","cross_cats_sorted":[],"title_canon_sha256":"4215f3c9f4346d7559507a3b74279d056c6dfc2af8da260c12910da5ff39fe74","abstract_canon_sha256":"0ca86ea45a2e50117b90b2392f6a44f34b6b680f5d2b8dc42ef0d7775d90475c"},"schema_version":"1.0"},"canonical_sha256":"94ef55d9f5baea95a715d118350ef30cb4dd0706571a081c6980e243c1b8c620","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:38.204987Z","signature_b64":"OlKHSoaEaE5vfOdRz5VcdL9lnIUyjlJIzbjmEQcbckFXIqRcyQpbeTGytasNBImJtyruClyAAKxchoaNhAyeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ef55d9f5baea95a715d118350ef30cb4dd0706571a081c6980e243c1b8c620","last_reissued_at":"2026-07-05T06:33:38.204577Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:38.204577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05619","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOKzaAoOJ094dG5KBYHO3ZNMp13y1Sj3QIYpX25Ezn0ANZNnh7o/AdPgwlwsePdfLzVT88MfRG3aeT7CoAHoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:49:15.868698Z"},"content_sha256":"93dbc0cd1f994d436ac8dfe6c2fad066677dbd3b27a57ea0bf7f71c95f847dd8","schema_version":"1.0","event_id":"sha256:93dbc0cd1f994d436ac8dfe6c2fad066677dbd3b27a57ea0bf7f71c95f847dd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:STXVLWPVXLVJLJYV2EMDKDXTBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential calculus over double Lie algebroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sophie Chemla","submitted_at":"2017-12-15T11:15:08Z","abstract_excerpt":"The notion of double Lie algebroid was defined by M. Van den Bergh and was illustrated by the double quasi Poisson case. We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative de Rham complex and the double Poisson-Lichnerowicz cohomology (Pichereau-vanWeyer) as particular cases of our construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05619","kind":"arxiv","version":3},"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/1712.05619/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kZWByEgdfVJZ2B74Zv6SzsTgK+uut/bOXDXz3W7WlKnbbAbNLhieW3D/tUAvqUWj4hVE70yHIUjX/QQ2DG5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:49:15.869078Z"},"content_sha256":"ef490460deb3f6946a66690f943ca8814d3337b61bb79291235322242830382e","schema_version":"1.0","event_id":"sha256:ef490460deb3f6946a66690f943ca8814d3337b61bb79291235322242830382e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/bundle.json","state_url":"https://pith.science/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T19:49:15Z","links":{"resolver":"https://pith.science/pith/STXVLWPVXLVJLJYV2EMDKDXTBS","bundle":"https://pith.science/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/bundle.json","state":"https://pith.science/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STXVLWPVXLVJLJYV2EMDKDXTBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:STXVLWPVXLVJLJYV2EMDKDXTBS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0ca86ea45a2e50117b90b2392f6a44f34b6b680f5d2b8dc42ef0d7775d90475c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2017-12-15T11:15:08Z","title_canon_sha256":"4215f3c9f4346d7559507a3b74279d056c6dfc2af8da260c12910da5ff39fe74"},"schema_version":"1.0","source":{"id":"1712.05619","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05619","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05619v3","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05619","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"STXVLWPVXLVJ","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_16","alias_value":"STXVLWPVXLVJLJYV","created_at":"2026-07-05T06:33:38Z"},{"alias_kind":"pith_short_8","alias_value":"STXVLWPV","created_at":"2026-07-05T06:33:38Z"}],"graph_snapshots":[{"event_id":"sha256:ef490460deb3f6946a66690f943ca8814d3337b61bb79291235322242830382e","target":"graph","created_at":"2026-07-05T06:33:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1712.05619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The notion of double Lie algebroid was defined by M. Van den Bergh and was illustrated by the double quasi Poisson case. We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative de Rham complex and the double Poisson-Lichnerowicz cohomology (Pichereau-vanWeyer) as particular cases of our construction.","authors_text":"Sophie Chemla","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2017-12-15T11:15:08Z","title":"Differential calculus over double Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05619","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:93dbc0cd1f994d436ac8dfe6c2fad066677dbd3b27a57ea0bf7f71c95f847dd8","target":"record","created_at":"2026-07-05T06:33:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0ca86ea45a2e50117b90b2392f6a44f34b6b680f5d2b8dc42ef0d7775d90475c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2017-12-15T11:15:08Z","title_canon_sha256":"4215f3c9f4346d7559507a3b74279d056c6dfc2af8da260c12910da5ff39fe74"},"schema_version":"1.0","source":{"id":"1712.05619","kind":"arxiv","version":3}},"canonical_sha256":"94ef55d9f5baea95a715d118350ef30cb4dd0706571a081c6980e243c1b8c620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ef55d9f5baea95a715d118350ef30cb4dd0706571a081c6980e243c1b8c620","first_computed_at":"2026-07-05T06:33:38.204577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:38.204577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OlKHSoaEaE5vfOdRz5VcdL9lnIUyjlJIzbjmEQcbckFXIqRcyQpbeTGytasNBImJtyruClyAAKxchoaNhAyeAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:38.204987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05619","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93dbc0cd1f994d436ac8dfe6c2fad066677dbd3b27a57ea0bf7f71c95f847dd8","sha256:ef490460deb3f6946a66690f943ca8814d3337b61bb79291235322242830382e"],"state_sha256":"ecb81539d2f49ae2382d0f37d41fc68177dfa2036749bac82cecd1a588f575fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cTdzdTnYKkg39ESG2jKSP3A1RXVuGWkQ0JudjOszClx14pWljrpodJ7WGLOT7gGX171mLZwJuQ/EF2HVWPpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T19:49:15.872044Z","bundle_sha256":"e121525886014e1fdbceef08f5d25e0fc3d1cb322fb22ad0c3d116ae51f3c2b4"}}