{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QH2YURDHT35L27YGEVXIPEDVW7","short_pith_number":"pith:QH2YURDH","canonical_record":{"source":{"id":"1304.6049","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T18:34:12Z","cross_cats_sorted":[],"title_canon_sha256":"3f8f2b51a8d969f4d396ff8be1c8090a4d2605b59d7455e923e1c53695d8d7e7","abstract_canon_sha256":"4ba4681698cccf1fd43afb635d657ad32e840792c6e293e20d9b358c28e4f54d"},"schema_version":"1.0"},"canonical_sha256":"81f58a44679efabd7f06256e879075b7d110686fa36661014950f8912777f26d","source":{"kind":"arxiv","id":"1304.6049","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6049","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6049v3","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6049","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"QH2YURDHT35L","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QH2YURDHT35L27YG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QH2YURDH","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QH2YURDHT35L27YGEVXIPEDVW7","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6049","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T18:34:12Z","cross_cats_sorted":[],"title_canon_sha256":"3f8f2b51a8d969f4d396ff8be1c8090a4d2605b59d7455e923e1c53695d8d7e7","abstract_canon_sha256":"4ba4681698cccf1fd43afb635d657ad32e840792c6e293e20d9b358c28e4f54d"},"schema_version":"1.0"},"canonical_sha256":"81f58a44679efabd7f06256e879075b7d110686fa36661014950f8912777f26d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.382473Z","signature_b64":"Nij/vQ5q9HrdVcOL3akHIxBb+DBsHWELVz0WWDqYYW8bsrm0SiPtJnu3lGkGeje2eZYSpprPRf0/fXC63AueBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81f58a44679efabd7f06256e879075b7d110686fa36661014950f8912777f26d","last_reissued_at":"2026-05-18T02:43:26.381895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.381895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6049","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ysXj1rUzZb8+XSth1PIE9fjAtKe/ans4NFtmmjj+OqBSSpwnKVZIm7avBCMiN3Ab1+gUeyhNGH68n9/t41MwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:15:28.831081Z"},"content_sha256":"747282c4095b91945ba201240d3952ebafcd091ab8a46b1a5c17c18c21550490","schema_version":"1.0","event_id":"sha256:747282c4095b91945ba201240d3952ebafcd091ab8a46b1a5c17c18c21550490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QH2YURDHT35L27YGEVXIPEDVW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A model structure on relative dg-Lie algebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gabriele Vezzosi","submitted_at":"2013-04-22T18:34:12Z","abstract_excerpt":"In this Note, for the future purposes of relative formal derived deformation theory and of derived coisotropic structures, we prove the existence of a model structure on the category of dg-Lie algebroids over a cochain differential non-positively graded commutative algebra over a commutative base ring k of characteristic 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6049","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/egmD6iqB3/k4k2/VE5OeTvfrPWwWZvDHMEKZxyXPDoq9lFNYS7tnDlWF68e/J41tp1gpZ/+6bKG3AyEidy0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:15:28.831723Z"},"content_sha256":"68962806a7d231b6416cbc6f75ca9ee131f8ad3aa3965b4a8512759413cefecd","schema_version":"1.0","event_id":"sha256:68962806a7d231b6416cbc6f75ca9ee131f8ad3aa3965b4a8512759413cefecd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QH2YURDHT35L27YGEVXIPEDVW7/bundle.json","state_url":"https://pith.science/pith/QH2YURDHT35L27YGEVXIPEDVW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QH2YURDHT35L27YGEVXIPEDVW7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T00:15:28Z","links":{"resolver":"https://pith.science/pith/QH2YURDHT35L27YGEVXIPEDVW7","bundle":"https://pith.science/pith/QH2YURDHT35L27YGEVXIPEDVW7/bundle.json","state":"https://pith.science/pith/QH2YURDHT35L27YGEVXIPEDVW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QH2YURDHT35L27YGEVXIPEDVW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QH2YURDHT35L27YGEVXIPEDVW7","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":"4ba4681698cccf1fd43afb635d657ad32e840792c6e293e20d9b358c28e4f54d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T18:34:12Z","title_canon_sha256":"3f8f2b51a8d969f4d396ff8be1c8090a4d2605b59d7455e923e1c53695d8d7e7"},"schema_version":"1.0","source":{"id":"1304.6049","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6049","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6049v3","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6049","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"QH2YURDHT35L","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QH2YURDHT35L27YG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QH2YURDH","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:68962806a7d231b6416cbc6f75ca9ee131f8ad3aa3965b4a8512759413cefecd","target":"graph","created_at":"2026-05-18T02:43:26Z","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, for the future purposes of relative formal derived deformation theory and of derived coisotropic structures, we prove the existence of a model structure on the category of dg-Lie algebroids over a cochain differential non-positively graded commutative algebra over a commutative base ring k of characteristic 0.","authors_text":"Gabriele Vezzosi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T18:34:12Z","title":"A model structure on relative dg-Lie algebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6049","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":"sha256:747282c4095b91945ba201240d3952ebafcd091ab8a46b1a5c17c18c21550490","target":"record","created_at":"2026-05-18T02:43:26Z","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":"4ba4681698cccf1fd43afb635d657ad32e840792c6e293e20d9b358c28e4f54d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T18:34:12Z","title_canon_sha256":"3f8f2b51a8d969f4d396ff8be1c8090a4d2605b59d7455e923e1c53695d8d7e7"},"schema_version":"1.0","source":{"id":"1304.6049","kind":"arxiv","version":3}},"canonical_sha256":"81f58a44679efabd7f06256e879075b7d110686fa36661014950f8912777f26d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81f58a44679efabd7f06256e879075b7d110686fa36661014950f8912777f26d","first_computed_at":"2026-05-18T02:43:26.381895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:26.381895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nij/vQ5q9HrdVcOL3akHIxBb+DBsHWELVz0WWDqYYW8bsrm0SiPtJnu3lGkGeje2eZYSpprPRf0/fXC63AueBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:26.382473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6049","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:747282c4095b91945ba201240d3952ebafcd091ab8a46b1a5c17c18c21550490","sha256:68962806a7d231b6416cbc6f75ca9ee131f8ad3aa3965b4a8512759413cefecd"],"state_sha256":"cc3ed5eafde802d035860dd8343cfa1dd22368f19458029b16cc117a287ba454"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTzelb86x4QW+hxh7ZOabx3jPY5GJZOfFa9H97HyK7alOqZ1Q+3H64V3vPZSj0m6IPf8lG1pwGjFmC03pJBMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:15:28.834962Z","bundle_sha256":"ff0154925647c1ef50fc68932078de976d6920b1538f8822aa9537d0abf67f23"}}