{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZOYY4YD5DJRZAYHMOWB3BXWFG6","short_pith_number":"pith:ZOYY4YD5","canonical_record":{"source":{"id":"0901.0322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-03T13:21:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"036c5b8b8aaaa90957519d447eb02e92c82830f76272491460387a4bf3e41df7","abstract_canon_sha256":"f78c1e9b561ec7e7b5ca305973f00c0d3f785fa42ecca19f40342d70248258d0"},"schema_version":"1.0"},"canonical_sha256":"cbb18e607d1a639060ec7583b0dec537876bcc3c2e6c89f96719628d6721b335","source":{"kind":"arxiv","id":"0901.0322","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0322","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0322v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0322","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZOYY4YD5DJRZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZOYY4YD5DJRZAYHM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZOYY4YD5","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZOYY4YD5DJRZAYHMOWB3BXWFG6","target":"record","payload":{"canonical_record":{"source":{"id":"0901.0322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-03T13:21:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"036c5b8b8aaaa90957519d447eb02e92c82830f76272491460387a4bf3e41df7","abstract_canon_sha256":"f78c1e9b561ec7e7b5ca305973f00c0d3f785fa42ecca19f40342d70248258d0"},"schema_version":"1.0"},"canonical_sha256":"cbb18e607d1a639060ec7583b0dec537876bcc3c2e6c89f96719628d6721b335","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.026157Z","signature_b64":"C+a6HBxf9dO0SORBfxY78Hl20CI7ovzKhAqVC8icpkUqyxlitdJ+RHpTeHInPlNnwYD4eIyyMRFrV64OdkX6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbb18e607d1a639060ec7583b0dec537876bcc3c2e6c89f96719628d6721b335","last_reissued_at":"2026-05-18T04:30:03.025582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.025582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.0322","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/Im2iQoknMXJ2ePjhGMCDDcbI2ev9dHE3D2RBiG83icCT7kwZwdNcRn3LHmOL/w7u0s+SfLrcTVXnWvLycnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:20:30.657570Z"},"content_sha256":"4a28ed5dabd239143c3fd7aaa7d4c664bafc4a49e708764f6a201bf36d33a75b","schema_version":"1.0","event_id":"sha256:4a28ed5dabd239143c3fd7aaa7d4c664bafc4a49e708764f6a201bf36d33a75b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZOYY4YD5DJRZAYHMOWB3BXWFG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Weil algebra and the Van Est isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Camilo Arias Abad, Marius Crainic","submitted_at":"2009-01-03T13:21:21Z","abstract_excerpt":"This paper belongs to a series devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman's BRST model, here we introduce the Weil algebra $W(A)$ associated to any Lie algebroid $A$. We then show that this Weil algebra is related to the Bott-Shulman-Stasheff complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more conceptual proof of the main result of Bursztyn et.al. on the reconstructions of multiplicative forms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0322","kind":"arxiv","version":2},"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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fk3KtLhLiCHGXN/e2yXQyOHik9wYkXteOgfQQRe8Sy/qB2+osoiQjJn9B2aJF3rijSPnf97b+lEGGx+guNOjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:20:30.658264Z"},"content_sha256":"1d504a70cc71f95e87ffee9291c055aa23beeeddcdec1d063e70bddad3f87f9a","schema_version":"1.0","event_id":"sha256:1d504a70cc71f95e87ffee9291c055aa23beeeddcdec1d063e70bddad3f87f9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/bundle.json","state_url":"https://pith.science/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/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":"2026-05-24T00:20:30Z","links":{"resolver":"https://pith.science/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6","bundle":"https://pith.science/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/bundle.json","state":"https://pith.science/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOYY4YD5DJRZAYHMOWB3BXWFG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZOYY4YD5DJRZAYHMOWB3BXWFG6","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":"f78c1e9b561ec7e7b5ca305973f00c0d3f785fa42ecca19f40342d70248258d0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-03T13:21:21Z","title_canon_sha256":"036c5b8b8aaaa90957519d447eb02e92c82830f76272491460387a4bf3e41df7"},"schema_version":"1.0","source":{"id":"0901.0322","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0322","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0322v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0322","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZOYY4YD5DJRZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZOYY4YD5DJRZAYHM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZOYY4YD5","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:1d504a70cc71f95e87ffee9291c055aa23beeeddcdec1d063e70bddad3f87f9a","target":"graph","created_at":"2026-05-18T04:30:03Z","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":"This paper belongs to a series devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman's BRST model, here we introduce the Weil algebra $W(A)$ associated to any Lie algebroid $A$. We then show that this Weil algebra is related to the Bott-Shulman-Stasheff complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more conceptual proof of the main result of Bursztyn et.al. on the reconstructions of multiplicative forms a","authors_text":"Camilo Arias Abad, Marius Crainic","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-03T13:21:21Z","title":"The Weil algebra and the Van Est isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0322","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":"sha256:4a28ed5dabd239143c3fd7aaa7d4c664bafc4a49e708764f6a201bf36d33a75b","target":"record","created_at":"2026-05-18T04:30:03Z","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":"f78c1e9b561ec7e7b5ca305973f00c0d3f785fa42ecca19f40342d70248258d0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-03T13:21:21Z","title_canon_sha256":"036c5b8b8aaaa90957519d447eb02e92c82830f76272491460387a4bf3e41df7"},"schema_version":"1.0","source":{"id":"0901.0322","kind":"arxiv","version":2}},"canonical_sha256":"cbb18e607d1a639060ec7583b0dec537876bcc3c2e6c89f96719628d6721b335","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbb18e607d1a639060ec7583b0dec537876bcc3c2e6c89f96719628d6721b335","first_computed_at":"2026-05-18T04:30:03.025582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.025582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C+a6HBxf9dO0SORBfxY78Hl20CI7ovzKhAqVC8icpkUqyxlitdJ+RHpTeHInPlNnwYD4eIyyMRFrV64OdkX6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.026157Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0322","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a28ed5dabd239143c3fd7aaa7d4c664bafc4a49e708764f6a201bf36d33a75b","sha256:1d504a70cc71f95e87ffee9291c055aa23beeeddcdec1d063e70bddad3f87f9a"],"state_sha256":"41f27435bfa67bd3eb852538b2d0a98f6d8ef5384eeef4394230732607909a81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaqzqUbGIdVmScXB49yPO+u6urYqc0hBKdCelHWD/dQiyy7/5wencK5ZA0D6wW1BXcCoc3JNv72CoFs8v/yUDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T00:20:30.661683Z","bundle_sha256":"5cc3176945b628d9345c7500c12e3e1c657068835eb9ed4a3bc44a900eb43cd3"}}