{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QVLV2Y4FZ4NWZSKMSK422DN7O5","short_pith_number":"pith:QVLV2Y4F","canonical_record":{"source":{"id":"1508.07865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T15:19:54Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"aa90e039143a57f193132cff1383f92cd1bc61e7337826ecefe014c7295a2643","abstract_canon_sha256":"8e2391d2652abe88dd1feca4023ac833fc59ae3682274a913a1bd5cfbe78eb36"},"schema_version":"1.0"},"canonical_sha256":"85575d6385cf1b6cc94c92b9ad0dbf77667cb50becb63e201318772d9d5d635c","source":{"kind":"arxiv","id":"1508.07865","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07865","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07865v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07865","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"QVLV2Y4FZ4NW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVLV2Y4FZ4NWZSKM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVLV2Y4F","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QVLV2Y4FZ4NWZSKMSK422DN7O5","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T15:19:54Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"aa90e039143a57f193132cff1383f92cd1bc61e7337826ecefe014c7295a2643","abstract_canon_sha256":"8e2391d2652abe88dd1feca4023ac833fc59ae3682274a913a1bd5cfbe78eb36"},"schema_version":"1.0"},"canonical_sha256":"85575d6385cf1b6cc94c92b9ad0dbf77667cb50becb63e201318772d9d5d635c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:31.298085Z","signature_b64":"doiHLr671GOdIrJhcGduLxOYMcgeu1FbQzFGkfjio2b5Wtf41iRl3LOIZ0x8ehdQ3vBEIxwqI/fJ6qpOiT5IBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85575d6385cf1b6cc94c92b9ad0dbf77667cb50becb63e201318772d9d5d635c","last_reissued_at":"2026-05-18T01:34:31.297613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:31.297613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07865","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B1Zq2tySRsjl6EWSekX8zmtNQDkvAec8f7hGXjW1DAZhngUVAgZKdbp3Ywa63+9GmJYsoCeOT1o9C4ROxmKSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:39:53.461302Z"},"content_sha256":"2b9a07f53ea2b824bbad6d9c0c17e9c85b1fbf488d95c082317dcb2d4d42429b","schema_version":"1.0","event_id":"sha256:2b9a07f53ea2b824bbad6d9c0c17e9c85b1fbf488d95c082317dcb2d4d42429b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QVLV2Y4FZ4NWZSKMSK422DN7O5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Generalized Lie Bialgebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Apurba Das","submitted_at":"2015-08-31T15:19:54Z","abstract_excerpt":"An alternative proof of the duality of generalized Lie bialgebroid is given and proved a canonical Jacobi structure can be defined on the base of it. We also introduce the notion of morphism between generalized Lie bialgebroids and proved that the induced Jacobi structure is unique upto a morphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07865","kind":"arxiv","version":1},"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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tO1jhAI2IXOQitGQFUplULeC/RD0SuU701Ji4Heme/2bw0or2Go0niXV/HHBSiH66ytWhtZO/KCO9iLjGa8wCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:39:53.461757Z"},"content_sha256":"9068b8bc58f5521a016279da84ce896405efe8dd7d758c23de4bb66efc793979","schema_version":"1.0","event_id":"sha256:9068b8bc58f5521a016279da84ce896405efe8dd7d758c23de4bb66efc793979"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/bundle.json","state_url":"https://pith.science/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/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":"2026-06-10T23:39:53Z","links":{"resolver":"https://pith.science/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5","bundle":"https://pith.science/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/bundle.json","state":"https://pith.science/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVLV2Y4FZ4NWZSKMSK422DN7O5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QVLV2Y4FZ4NWZSKMSK422DN7O5","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":"8e2391d2652abe88dd1feca4023ac833fc59ae3682274a913a1bd5cfbe78eb36","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T15:19:54Z","title_canon_sha256":"aa90e039143a57f193132cff1383f92cd1bc61e7337826ecefe014c7295a2643"},"schema_version":"1.0","source":{"id":"1508.07865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07865","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07865v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07865","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"QVLV2Y4FZ4NW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVLV2Y4FZ4NWZSKM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVLV2Y4F","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:9068b8bc58f5521a016279da84ce896405efe8dd7d758c23de4bb66efc793979","target":"graph","created_at":"2026-05-18T01:34:31Z","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":"An alternative proof of the duality of generalized Lie bialgebroid is given and proved a canonical Jacobi structure can be defined on the base of it. We also introduce the notion of morphism between generalized Lie bialgebroids and proved that the induced Jacobi structure is unique upto a morphism.","authors_text":"Apurba Das","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T15:19:54Z","title":"On Generalized Lie Bialgebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07865","kind":"arxiv","version":1},"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":"sha256:2b9a07f53ea2b824bbad6d9c0c17e9c85b1fbf488d95c082317dcb2d4d42429b","target":"record","created_at":"2026-05-18T01:34:31Z","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":"8e2391d2652abe88dd1feca4023ac833fc59ae3682274a913a1bd5cfbe78eb36","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T15:19:54Z","title_canon_sha256":"aa90e039143a57f193132cff1383f92cd1bc61e7337826ecefe014c7295a2643"},"schema_version":"1.0","source":{"id":"1508.07865","kind":"arxiv","version":1}},"canonical_sha256":"85575d6385cf1b6cc94c92b9ad0dbf77667cb50becb63e201318772d9d5d635c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85575d6385cf1b6cc94c92b9ad0dbf77667cb50becb63e201318772d9d5d635c","first_computed_at":"2026-05-18T01:34:31.297613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:31.297613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"doiHLr671GOdIrJhcGduLxOYMcgeu1FbQzFGkfjio2b5Wtf41iRl3LOIZ0x8ehdQ3vBEIxwqI/fJ6qpOiT5IBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:31.298085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9a07f53ea2b824bbad6d9c0c17e9c85b1fbf488d95c082317dcb2d4d42429b","sha256:9068b8bc58f5521a016279da84ce896405efe8dd7d758c23de4bb66efc793979"],"state_sha256":"32f93fbd70922af60549bc9d6ca53bbb58004d72244290996f4e28e5c7557a2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRtWYDsQoH2x5XyDCusObGz7bJXL8xkSNqy7BviGIKmtY1uaFYV7AkfDnsTP3O3IS4jQDMwUkfH93DxFsu+IDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:39:53.465039Z","bundle_sha256":"1ed5a77f2847840f9a08630fddea35e100a33921f09ea4f67f622bf9b6897a26"}}