{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NZZPORH2IFEYYI7HQFX777CNGU","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":"b9a57f99399cfdd9c071c0917abdcd895019d449fa361fe98a49bc678fb35635","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-08-10T12:04:53Z","title_canon_sha256":"41b2c4b2573862778e7eb752546a706326988aed60dd922dbc97e638d6276348"},"schema_version":"1.0","source":{"id":"1708.03174","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03174","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03174v3","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03174","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"NZZPORH2IFEY","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZZPORH2IFEYYI7H","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZZPORH2","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:9feb26fb5704d2924205b88a2fa7ad75833bd776e8d290a33e5035058ec696a9","target":"graph","created_at":"2026-05-17T23:57:15Z","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 introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach higher algebroids are vector bundle comorphism between graded-linear bundles satisfying natural axioms. We provide natural examples and discuss applications in geometric mechanics.","authors_text":"Micha{\\l} J\\'o\\'zwikowski, Miko{\\l}aj Rotkiewicz","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-08-10T12:04:53Z","title":"Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03174","kind":"arxiv","version":3},"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:e950749b838d2178254dc4d59835292c5fc7d3d234cfeaf940c858cafd753016","target":"record","created_at":"2026-05-17T23:57:15Z","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":"b9a57f99399cfdd9c071c0917abdcd895019d449fa361fe98a49bc678fb35635","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-08-10T12:04:53Z","title_canon_sha256":"41b2c4b2573862778e7eb752546a706326988aed60dd922dbc97e638d6276348"},"schema_version":"1.0","source":{"id":"1708.03174","kind":"arxiv","version":3}},"canonical_sha256":"6e72f744fa41498c23e7816ffffc4d3510758f18db93030609b30882f94bd633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e72f744fa41498c23e7816ffffc4d3510758f18db93030609b30882f94bd633","first_computed_at":"2026-05-17T23:57:15.656988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:15.656988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pAwNILj+W/elIk4MrmMz1EeTi2uoGZIgv1vztfrgizTaUJwXN/ALYW+IYMATlQjaFO/MCYTDhyES3ghHSmuSAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:15.657627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03174","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e950749b838d2178254dc4d59835292c5fc7d3d234cfeaf940c858cafd753016","sha256:9feb26fb5704d2924205b88a2fa7ad75833bd776e8d290a33e5035058ec696a9"],"state_sha256":"645b8e7299758db077a611a439a759e80fcb7cb1f8edc32683decb1587b9e7ac"}