{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7NLPKF75A2YA5HQ67PA2BMNTEZ","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":"85a63c7379eb4ca7f386c4e9278af0d17a4b4f9552959d490bc266a4942b0e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-07-22T23:21:54Z","title_canon_sha256":"fd2506b31745b430a1843f492cfa3243156d2b2a53be528ad5de286117842ae0"},"schema_version":"1.0","source":{"id":"1807.08382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08382","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08382v1","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08382","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"7NLPKF75A2YA","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7NLPKF75A2YA5HQ6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7NLPKF75","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:5f0a776711763f4d7c5c54eb3e91d46876abfd28f67b61bab24088d03ddfed64","target":"graph","created_at":"2026-05-17T23:53:29Z","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":"In this note, we examine the bundle picture of the pullback construction of Lie algebroids. The notion of submersions by Lie algebroids is introduced, which leads to a new proof of the local normal form for lie algebroid transversals of [Bursztyn et al., Crelle, 2017], and which we use to deduce that Lie algebroids transversals concentrate all local cohomology.\n  The locally trivial version of submersions by Lie algebroids $\\mathfrak{S}$ is then discussed, and we show that this notion is equivalent to the existence of a complete Ehresmann connection for $\\mathfrak{S}$, extending the main resul","authors_text":"Pedro Frejlich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-07-22T23:21:54Z","title":"Submersions by Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08382","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":"sha256:1ee9ce6375cc223e8189145a1430385b29606413b18348863f93d060dd2f2835","target":"record","created_at":"2026-05-17T23:53:29Z","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":"85a63c7379eb4ca7f386c4e9278af0d17a4b4f9552959d490bc266a4942b0e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-07-22T23:21:54Z","title_canon_sha256":"fd2506b31745b430a1843f492cfa3243156d2b2a53be528ad5de286117842ae0"},"schema_version":"1.0","source":{"id":"1807.08382","kind":"arxiv","version":1}},"canonical_sha256":"fb56f517fd06b00e9e1efbc1a0b1b32646b4a10cd390709f05c64f4b3e80ac8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb56f517fd06b00e9e1efbc1a0b1b32646b4a10cd390709f05c64f4b3e80ac8e","first_computed_at":"2026-05-17T23:53:29.853691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:29.853691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ALBekYcJirDYHC69KL39/T6gzReGWPmR0DmNqDm0bfqU/z/OVIB2LECmHbhBJRjUKZN0IXRBuFhfBV/wsKI/Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:29.854237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ee9ce6375cc223e8189145a1430385b29606413b18348863f93d060dd2f2835","sha256:5f0a776711763f4d7c5c54eb3e91d46876abfd28f67b61bab24088d03ddfed64"],"state_sha256":"f560ee11a773dacc146426c9cee7fb1f75e51d4c4ca23897cdbaeaf5d05c5e88"}