{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OE4HN72JHGIL7QV6UJNQMYUARE","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":"782480db5adc9ce7efeeb3009c50e90836cff3649590b342c798872544ebf7e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-07T23:58:41Z","title_canon_sha256":"1e09c4a11243f212f650e13f041499319257a5532b5bedfa772dc1babab3504d"},"schema_version":"1.0","source":{"id":"1107.1539","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1539","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1539v3","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1539","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"OE4HN72JHGIL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OE4HN72JHGIL7QV6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OE4HN72J","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:f66baefd0869f4ed30d4af2db282c871bae6287097fc11ddc8a407403efe35b7","target":"graph","created_at":"2026-05-18T02:28:48Z","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 establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaintrob's Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.","authors_text":"Rajan Amit Mehta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-07T23:58:41Z","title":"Lie algebroid modules and representations up to homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1539","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":"sha256:13c9b80ac8f537927eb436bacb378b82b8db213b37c0b51b5b02d2424ced512b","target":"record","created_at":"2026-05-18T02:28:48Z","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":"782480db5adc9ce7efeeb3009c50e90836cff3649590b342c798872544ebf7e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-07T23:58:41Z","title_canon_sha256":"1e09c4a11243f212f650e13f041499319257a5532b5bedfa772dc1babab3504d"},"schema_version":"1.0","source":{"id":"1107.1539","kind":"arxiv","version":3}},"canonical_sha256":"713876ff493990bfc2bea25b0662808905f2932c7d125bc9f0e9002777f5fd61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"713876ff493990bfc2bea25b0662808905f2932c7d125bc9f0e9002777f5fd61","first_computed_at":"2026-05-18T02:28:48.571283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:48.571283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAk677Bkk60qyZ/z8ucZOVNMiiGllRxnSpjMzqF865yDYG8UObHKUVJhV4MHjhZirgMox4j/b7CQozi565bCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:48.571652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1539","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13c9b80ac8f537927eb436bacb378b82b8db213b37c0b51b5b02d2424ced512b","sha256:f66baefd0869f4ed30d4af2db282c871bae6287097fc11ddc8a407403efe35b7"],"state_sha256":"2640c87fe532a8cd1df39ea827df93e9233f2cd98f87d53c3bda55cd61b6aec4"}