{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U7OIM3IV5GQ6NEHX7CGSYJXAV7","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":"81cb3e3c7de63201630ab4cbbf9e333750a6ca516c6c5acd78464c2a3b2cf48b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-16T15:01:59Z","title_canon_sha256":"fe59df9344a84c8ce5f3ed99af042cbba17ad271f2c0db5adb5ecf9b20250d22"},"schema_version":"1.0","source":{"id":"1210.4443","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4443","created_at":"2026-07-05T00:37:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4443v2","created_at":"2026-07-05T00:37:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4443","created_at":"2026-07-05T00:37:24Z"},{"alias_kind":"pith_short_12","alias_value":"U7OIM3IV5GQ6","created_at":"2026-07-05T00:37:24Z"},{"alias_kind":"pith_short_16","alias_value":"U7OIM3IV5GQ6NEHX","created_at":"2026-07-05T00:37:24Z"},{"alias_kind":"pith_short_8","alias_value":"U7OIM3IV","created_at":"2026-07-05T00:37:24Z"}],"graph_snapshots":[{"event_id":"sha256:3c9eeb61cbe75df7aaebd951594339e5cf2b67953547379340af8fdc90376202","target":"graph","created_at":"2026-07-05T00:37:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1210.4443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the category of integrable Lie algebroids and complete Lie algebroid comorphisms to the category of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of comorphisms and Poisson maps may not hold in the absence of a completeness assumption.","authors_text":"Alan Weinstein, Alberto S. Cattaneo, Benoit Dherin","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-16T15:01:59Z","title":"Integration of Lie Algebroid Comorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4443","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":"sha256:93d57e07bca8b55bf090c1efc3eb14672703216c731d4ff846a75f36c603f773","target":"record","created_at":"2026-07-05T00:37:24Z","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":"81cb3e3c7de63201630ab4cbbf9e333750a6ca516c6c5acd78464c2a3b2cf48b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-16T15:01:59Z","title_canon_sha256":"fe59df9344a84c8ce5f3ed99af042cbba17ad271f2c0db5adb5ecf9b20250d22"},"schema_version":"1.0","source":{"id":"1210.4443","kind":"arxiv","version":2}},"canonical_sha256":"a7dc866d15e9a1e690f7f88d2c26e0affc6fd5e850d0da17765c6fcde0a8d244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7dc866d15e9a1e690f7f88d2c26e0affc6fd5e850d0da17765c6fcde0a8d244","first_computed_at":"2026-07-05T00:37:24.635332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:24.635332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e7W7ENImHh+2kBc7NA8l1P+uuPfwlotvAQb48KSZsxXQo9A3TF6y4cpikvEVfwGL9ZRSNSl+b+fHtHnW4/VRAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:24.635838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4443","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93d57e07bca8b55bf090c1efc3eb14672703216c731d4ff846a75f36c603f773","sha256:3c9eeb61cbe75df7aaebd951594339e5cf2b67953547379340af8fdc90376202"],"state_sha256":"93e8622efc8f5260c4d8912c362ef18b707759854e76d104d7ee10682a30d8ee"}