{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7O7NS7JU5ZKFGP2NRQR3V7OPC5","short_pith_number":"pith:7O7NS7JU","schema_version":"1.0","canonical_sha256":"fbbed97d34ee54533f4d8c23bafdcf174555712e4c4297743de1ad845c8d09bd","source":{"kind":"arxiv","id":"1401.7468","version":1},"attestation_state":"computed","paper":{"title":"Modular Class of a Lie algebroid with a Nambu structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Apurba Das, Goutam Mukherjee, Shilpa Gondhali","submitted_at":"2014-01-29T11:00:30Z","abstract_excerpt":"In this paper, we introduce the notion of modular class of a Lie algebroid $A$ equipped with a Nambu structure satisfying some suitable hypothesis. We also introduce cohomology and homology theories for such Lie algebroids and prove that these theories are connected by a duality isomorphism when the modular class is null."},"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":"1401.7468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T11:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"2a00da4f0927ddf064564dd6beff9d255eba7e43ed39b3804fdac2f64ba7b76c","abstract_canon_sha256":"c5526c9f6f46f2377a4aa68da3158b89812251bb80eac25719b03c313573f1e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:48.313656Z","signature_b64":"SsCT/AzfT0DSLVFlt2pS6CcvhcoxhY/3MgFwypbldUZQsakdzZbC4/qfUTZAXOw4dAZTUghq5gnbEY260WzrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbbed97d34ee54533f4d8c23bafdcf174555712e4c4297743de1ad845c8d09bd","last_reissued_at":"2026-05-18T03:00:48.312899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:48.312899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular Class of a Lie algebroid with a Nambu structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Apurba Das, Goutam Mukherjee, Shilpa Gondhali","submitted_at":"2014-01-29T11:00:30Z","abstract_excerpt":"In this paper, we introduce the notion of modular class of a Lie algebroid $A$ equipped with a Nambu structure satisfying some suitable hypothesis. We also introduce cohomology and homology theories for such Lie algebroids and prove that these theories are connected by a duality isomorphism when the modular class is null."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7468","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.7468","created_at":"2026-05-18T03:00:48.313022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7468v1","created_at":"2026-05-18T03:00:48.313022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7468","created_at":"2026-05-18T03:00:48.313022+00:00"},{"alias_kind":"pith_short_12","alias_value":"7O7NS7JU5ZKF","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7O7NS7JU5ZKFGP2N","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7O7NS7JU","created_at":"2026-05-18T12:28:19.803747+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/7O7NS7JU5ZKFGP2NRQR3V7OPC5","json":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5.json","graph_json":"https://pith.science/api/pith-number/7O7NS7JU5ZKFGP2NRQR3V7OPC5/graph.json","events_json":"https://pith.science/api/pith-number/7O7NS7JU5ZKFGP2NRQR3V7OPC5/events.json","paper":"https://pith.science/paper/7O7NS7JU"},"agent_actions":{"view_html":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5","download_json":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5.json","view_paper":"https://pith.science/paper/7O7NS7JU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7468&json=true","fetch_graph":"https://pith.science/api/pith-number/7O7NS7JU5ZKFGP2NRQR3V7OPC5/graph.json","fetch_events":"https://pith.science/api/pith-number/7O7NS7JU5ZKFGP2NRQR3V7OPC5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5/action/storage_attestation","attest_author":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5/action/author_attestation","sign_citation":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5/action/citation_signature","submit_replication":"https://pith.science/pith/7O7NS7JU5ZKFGP2NRQR3V7OPC5/action/replication_record"}},"created_at":"2026-05-18T03:00:48.313022+00:00","updated_at":"2026-05-18T03:00:48.313022+00:00"}