{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GVRCESNBLJCAMJQ3OXWB2CAKSC","short_pith_number":"pith:GVRCESNB","schema_version":"1.0","canonical_sha256":"35622249a15a4406261b75ec1d080a9086bf966c4ff56f09504d8ddb2840e851","source":{"kind":"arxiv","id":"1610.09682","version":1},"attestation_state":"computed","paper":{"title":"On para-K\\\"ahler Lie algebroids and generalized pseudo-Hessian structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mohamed Boucetta, Sa\\\"id Benayadi","submitted_at":"2016-10-30T17:44:31Z","abstract_excerpt":"In this paper, we generalize all the results obtained on para-K\\\"ahler Lie algebras in Journal of Algebra {\\bf 436} (2015) 61-101 to para-K\\\"ahler Lie algebroids. In particular, we study exact para-K\\\"ahler Lie algebroids as a generalization of exact para-K\\\"ahler Lie algebras. This study leads to a natural generalization of pseudo-Hessian manifolds. Generalized pseudo-Hessian manifolds have many similarities with Poisson manifolds. We explore these similarities which, among others, leads to a powerful machinery to build examples of non trivial pseudo-Hessian structures. Namely, we will show t"},"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":"1610.09682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T17:44:31Z","cross_cats_sorted":[],"title_canon_sha256":"599f3f2c8669862d2fce6c9a4ca3f47b1709b2f8507578c8bfd83e0e9bef93c1","abstract_canon_sha256":"c25d7eb9da1e5bb73902b6b95ec3afbfab87f5cb007c0700745145e41c39b6d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:51.302692Z","signature_b64":"vb5+7Vkex+kYip+K/9te6O1RWbwFi8DjbNgTM6akksj53DIt8komN9TlH7oOxHyNdjJfry4ip9Wrrti8oSrYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35622249a15a4406261b75ec1d080a9086bf966c4ff56f09504d8ddb2840e851","last_reissued_at":"2026-05-18T01:00:51.302148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:51.302148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On para-K\\\"ahler Lie algebroids and generalized pseudo-Hessian structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mohamed Boucetta, Sa\\\"id Benayadi","submitted_at":"2016-10-30T17:44:31Z","abstract_excerpt":"In this paper, we generalize all the results obtained on para-K\\\"ahler Lie algebras in Journal of Algebra {\\bf 436} (2015) 61-101 to para-K\\\"ahler Lie algebroids. In particular, we study exact para-K\\\"ahler Lie algebroids as a generalization of exact para-K\\\"ahler Lie algebras. This study leads to a natural generalization of pseudo-Hessian manifolds. Generalized pseudo-Hessian manifolds have many similarities with Poisson manifolds. We explore these similarities which, among others, leads to a powerful machinery to build examples of non trivial pseudo-Hessian structures. Namely, we will show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09682","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":"1610.09682","created_at":"2026-05-18T01:00:51.302235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09682v1","created_at":"2026-05-18T01:00:51.302235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09682","created_at":"2026-05-18T01:00:51.302235+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVRCESNBLJCA","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVRCESNBLJCAMJQ3","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVRCESNB","created_at":"2026-05-18T12:30:19.053100+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/GVRCESNBLJCAMJQ3OXWB2CAKSC","json":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC.json","graph_json":"https://pith.science/api/pith-number/GVRCESNBLJCAMJQ3OXWB2CAKSC/graph.json","events_json":"https://pith.science/api/pith-number/GVRCESNBLJCAMJQ3OXWB2CAKSC/events.json","paper":"https://pith.science/paper/GVRCESNB"},"agent_actions":{"view_html":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC","download_json":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC.json","view_paper":"https://pith.science/paper/GVRCESNB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09682&json=true","fetch_graph":"https://pith.science/api/pith-number/GVRCESNBLJCAMJQ3OXWB2CAKSC/graph.json","fetch_events":"https://pith.science/api/pith-number/GVRCESNBLJCAMJQ3OXWB2CAKSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC/action/storage_attestation","attest_author":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC/action/author_attestation","sign_citation":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC/action/citation_signature","submit_replication":"https://pith.science/pith/GVRCESNBLJCAMJQ3OXWB2CAKSC/action/replication_record"}},"created_at":"2026-05-18T01:00:51.302235+00:00","updated_at":"2026-05-18T01:00:51.302235+00:00"}