{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EI2ZFGHS5OHB7NPDFDLDJ6C2JU","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":"327aea3591c13c946b9374c56cb8967d513b2aa9795fe50b658f5d2800019104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-03T11:19:15Z","title_canon_sha256":"ef6b97491dafcaecd9111939ff56d67b3e263a7472940acfaf53a4ab75f47528"},"schema_version":"1.0","source":{"id":"1111.0800","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0800","created_at":"2026-05-18T04:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0800v2","created_at":"2026-05-18T04:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0800","created_at":"2026-05-18T04:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"EI2ZFGHS5OHB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EI2ZFGHS5OHB7NPD","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EI2ZFGHS","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:4ed6548c8ff02957675dcd61bf03e864503e252bff193dde0bd8ea18895b714a","target":"graph","created_at":"2026-05-18T04:04:33Z","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 extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis, deformation-Nijenhuis and Nijenhuis pairs) that extend to Courant algebroids the notion of a Poisson-Nijenhuis manifold, by using the idea that both the Poisson and the Nijenhuis structures, although they seem to be different in nature when considered on manifolds, are just $(1,1)$-tensors on the usual Courant algebroid $TM \\oplus T^*M $ satisfying several constraints. For each of the generalizations mentione","authors_text":"Camille Laurent-Gengoux, Joana M. Nunes da Costa, Paulo Antunes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-03T11:19:15Z","title":"Hierarchies and compatibility on Courant algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0800","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":"sha256:3e950b7aa1f5ec6009f5b4570bfd3268dc64a8114f41350b91cab47f9e13126d","target":"record","created_at":"2026-05-18T04:04:33Z","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":"327aea3591c13c946b9374c56cb8967d513b2aa9795fe50b658f5d2800019104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-03T11:19:15Z","title_canon_sha256":"ef6b97491dafcaecd9111939ff56d67b3e263a7472940acfaf53a4ab75f47528"},"schema_version":"1.0","source":{"id":"1111.0800","kind":"arxiv","version":2}},"canonical_sha256":"22359298f2eb8e1fb5e328d634f85a4d28b0ddd011b696bff402cf22bd4d9548","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22359298f2eb8e1fb5e328d634f85a4d28b0ddd011b696bff402cf22bd4d9548","first_computed_at":"2026-05-18T04:04:33.031697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:33.031697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EgJ8g9fv/+xdBW8vcq1h7huUL9qurhUrRM15pQnR/Yq0yZgtrwK52SwyS8zbb2lEwSIf2TKJk/OB8l52accgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:33.032242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0800","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e950b7aa1f5ec6009f5b4570bfd3268dc64a8114f41350b91cab47f9e13126d","sha256:4ed6548c8ff02957675dcd61bf03e864503e252bff193dde0bd8ea18895b714a"],"state_sha256":"f1aba02ea8c97f5a8e29899874e29d537d2f21ce8a40647cc4bc5396eec9e6d3"}