{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TRUJJDTDW454LEG7X66PT2WL7Q","short_pith_number":"pith:TRUJJDTD","canonical_record":{"source":{"id":"1611.01613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-05T07:47:57Z","cross_cats_sorted":[],"title_canon_sha256":"ca60e4df7665e3d620549cbfabb5a5fbd00091ea7de52643b0cf73e3a194581e","abstract_canon_sha256":"d8d83a48d32a0267614e649350d7114abec19ae4bfe77501f8228a7f9c930d68"},"schema_version":"1.0"},"canonical_sha256":"9c68948e63b73bc590dfbfbcf9eacbfc12c1b0f138b16574b0415ab3952b9dd4","source":{"kind":"arxiv","id":"1611.01613","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01613","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01613v2","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01613","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"TRUJJDTDW454","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRUJJDTDW454LEG7","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRUJJDTD","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TRUJJDTDW454LEG7X66PT2WL7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-05T07:47:57Z","cross_cats_sorted":[],"title_canon_sha256":"ca60e4df7665e3d620549cbfabb5a5fbd00091ea7de52643b0cf73e3a194581e","abstract_canon_sha256":"d8d83a48d32a0267614e649350d7114abec19ae4bfe77501f8228a7f9c930d68"},"schema_version":"1.0"},"canonical_sha256":"9c68948e63b73bc590dfbfbcf9eacbfc12c1b0f138b16574b0415ab3952b9dd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:02.914699Z","signature_b64":"NIteuODTgphMfxvkBGAvZiPzO8kx0ja/zHo/30VJqG+FS05LnKYtbfL6SQ/uQrkV9t3KL9hmRnkmQGjwE8SfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c68948e63b73bc590dfbfbcf9eacbfc12c1b0f138b16574b0415ab3952b9dd4","last_reissued_at":"2026-05-18T00:51:02.914152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:02.914152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01613","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnB+yrlnSUJrJtm85/JUYUik7qrSVGU6IgUj2KNJSvEtp6jZEcOT5oKiCEnygt03ug9tvsu0fGqYOPYcx7JvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:03:48.509651Z"},"content_sha256":"f676def6cae03c76e39af5b0c65c41d5b1910b31077488a262b46edb595ebbf1","schema_version":"1.0","event_id":"sha256:f676def6cae03c76e39af5b0c65c41d5b1910b31077488a262b46edb595ebbf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TRUJJDTDW454LEG7X66PT2WL7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative Nambu structures on Lie groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Apurba Das","submitted_at":"2016-11-05T07:47:57Z","abstract_excerpt":"We study some properties of coisotropic submanifolds of a manifold with respect to a given multivector field. Using this notion, we generalize the results of Weinstein \\cite{wein} from Poisson bivector field to Nambu-Poisson tensor or more generally to any multivector field. We also introduce the notion of Nambu-Lie groupoid generalizing the concepts of both Poisson-Lie groupoid and Nambu-Lie group. We show that the infinitesimal version of Nambu-Lie groupoid is the notion of weak Lie-Filippov bialgebroid as introduced in \\cite{bas-bas-das-muk}. Next we introduce coisotropic subgroupoids of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01613","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaydOoRdRNkxl1I693s1+fEGV2kHuBaj9LaS/WGnvgAl6/Ws1pLz6KWELTE1ALa1QuNKjdpgTEJWdWhPHZalCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:03:48.510001Z"},"content_sha256":"8b91e67ba6997327458d66ed7864fa174ccbb820535ae8327773cabf541215eb","schema_version":"1.0","event_id":"sha256:8b91e67ba6997327458d66ed7864fa174ccbb820535ae8327773cabf541215eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRUJJDTDW454LEG7X66PT2WL7Q/bundle.json","state_url":"https://pith.science/pith/TRUJJDTDW454LEG7X66PT2WL7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRUJJDTDW454LEG7X66PT2WL7Q/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":"2026-06-11T02:03:48Z","links":{"resolver":"https://pith.science/pith/TRUJJDTDW454LEG7X66PT2WL7Q","bundle":"https://pith.science/pith/TRUJJDTDW454LEG7X66PT2WL7Q/bundle.json","state":"https://pith.science/pith/TRUJJDTDW454LEG7X66PT2WL7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRUJJDTDW454LEG7X66PT2WL7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TRUJJDTDW454LEG7X66PT2WL7Q","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":"d8d83a48d32a0267614e649350d7114abec19ae4bfe77501f8228a7f9c930d68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-05T07:47:57Z","title_canon_sha256":"ca60e4df7665e3d620549cbfabb5a5fbd00091ea7de52643b0cf73e3a194581e"},"schema_version":"1.0","source":{"id":"1611.01613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01613","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01613v2","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01613","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"TRUJJDTDW454","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRUJJDTDW454LEG7","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRUJJDTD","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:8b91e67ba6997327458d66ed7864fa174ccbb820535ae8327773cabf541215eb","target":"graph","created_at":"2026-05-18T00:51:02Z","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"},"paper":{"abstract_excerpt":"We study some properties of coisotropic submanifolds of a manifold with respect to a given multivector field. Using this notion, we generalize the results of Weinstein \\cite{wein} from Poisson bivector field to Nambu-Poisson tensor or more generally to any multivector field. We also introduce the notion of Nambu-Lie groupoid generalizing the concepts of both Poisson-Lie groupoid and Nambu-Lie group. We show that the infinitesimal version of Nambu-Lie groupoid is the notion of weak Lie-Filippov bialgebroid as introduced in \\cite{bas-bas-das-muk}. Next we introduce coisotropic subgroupoids of a ","authors_text":"Apurba Das","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-05T07:47:57Z","title":"Multiplicative Nambu structures on Lie groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01613","kind":"arxiv","version":2},"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:f676def6cae03c76e39af5b0c65c41d5b1910b31077488a262b46edb595ebbf1","target":"record","created_at":"2026-05-18T00:51:02Z","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":"d8d83a48d32a0267614e649350d7114abec19ae4bfe77501f8228a7f9c930d68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-05T07:47:57Z","title_canon_sha256":"ca60e4df7665e3d620549cbfabb5a5fbd00091ea7de52643b0cf73e3a194581e"},"schema_version":"1.0","source":{"id":"1611.01613","kind":"arxiv","version":2}},"canonical_sha256":"9c68948e63b73bc590dfbfbcf9eacbfc12c1b0f138b16574b0415ab3952b9dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c68948e63b73bc590dfbfbcf9eacbfc12c1b0f138b16574b0415ab3952b9dd4","first_computed_at":"2026-05-18T00:51:02.914152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:02.914152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NIteuODTgphMfxvkBGAvZiPzO8kx0ja/zHo/30VJqG+FS05LnKYtbfL6SQ/uQrkV9t3KL9hmRnkmQGjwE8SfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:02.914699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f676def6cae03c76e39af5b0c65c41d5b1910b31077488a262b46edb595ebbf1","sha256:8b91e67ba6997327458d66ed7864fa174ccbb820535ae8327773cabf541215eb"],"state_sha256":"949a7aa602efb6a64c4ea17c5de505fbc77bfb981ef7f419d07e0fd66d1635b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Pe76N144HKN5XecVPKamW/dZQs5kwFUpBogQUROvnvoT5ntAdoPvHPyiHexQstnIu9A9oNzdHrq3wjFVPDhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:03:48.512216Z","bundle_sha256":"df7df51f35e7405f90fda1151ab0d7a08fe49ffa2b22ab4415b33c18e22b4e89"}}