{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SDX6QQA7OPKQBXIXX4CZCAORK3","short_pith_number":"pith:SDX6QQA7","canonical_record":{"source":{"id":"1602.06887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T18:47:52Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2644b8c6be61f7d9e7cce3996648b962e471a4f17559d6ea57fc508e76bf7a1a","abstract_canon_sha256":"8df9a50f42860691cb553b11e93ab8210c14d49ddd42fdc68c09b321dd8b0ad7"},"schema_version":"1.0"},"canonical_sha256":"90efe8401f73d500dd17bf059101d156e64cd6ca7cd09027a4550653ba7f5399","source":{"kind":"arxiv","id":"1602.06887","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06887","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06887v1","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06887","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"SDX6QQA7OPKQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDX6QQA7OPKQBXIX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDX6QQA7","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SDX6QQA7OPKQBXIXX4CZCAORK3","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T18:47:52Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2644b8c6be61f7d9e7cce3996648b962e471a4f17559d6ea57fc508e76bf7a1a","abstract_canon_sha256":"8df9a50f42860691cb553b11e93ab8210c14d49ddd42fdc68c09b321dd8b0ad7"},"schema_version":"1.0"},"canonical_sha256":"90efe8401f73d500dd17bf059101d156e64cd6ca7cd09027a4550653ba7f5399","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:23.232841Z","signature_b64":"bwgUR6C0fGd/pmUd0VSYCTwna+/ElIJpr6XtAsj7bgP8ZLUiyO90guRwcPhiwxvG7q3P2wD77FWMWJFMiIJIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90efe8401f73d500dd17bf059101d156e64cd6ca7cd09027a4550653ba7f5399","last_reissued_at":"2026-05-18T00:34:23.232360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:23.232360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06887","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbnt00xHPm7HAGTcmHa7Fc5NtdWdXSCYCNu0rP6yvhJ+r0mjOR+AJfbsyqLPtHFEkQ6MjpXeL6/RsaKpGYmKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:33.371477Z"},"content_sha256":"59ddace6d864a5fa51d59207338522700ce911579709acd7ee39830509917bab","schema_version":"1.0","event_id":"sha256:59ddace6d864a5fa51d59207338522700ce911579709acd7ee39830509917bab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SDX6QQA7OPKQBXIXX4CZCAORK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Van Est isomorphism for homogeneous cochains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"Alejandro Cabrera, Thiago Drummond","submitted_at":"2016-02-22T18:47:52Z","abstract_excerpt":"VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by considering the complex of cochains which are k-homogeneous on the linear fiber. Our main result is a Van Est theorem for such cochains. We also work out two applications to the general theory of representations of Lie groupoids and algebroids. The case k=1 yields a Van Est map for representations up to homotopy on 2-term graded vector bundles. Arbitrary k-homogeneous cochains on suitable VB-groupoids lead to a novel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06887","kind":"arxiv","version":1},"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":"2026-05-18T00:34:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCQyLtdSxtW5TnIkHPflkI4ffdY4szsCXNOvSjQtZ5RDw46VXZSolXxYT+ZNTSBJ0KEsbGgLrFki5qTybwdeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:33.371823Z"},"content_sha256":"ae8cc466885a08d9c78228302506fd9c55ec71e5a54edb9bf2e1e87ce0a56cd4","schema_version":"1.0","event_id":"sha256:ae8cc466885a08d9c78228302506fd9c55ec71e5a54edb9bf2e1e87ce0a56cd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/bundle.json","state_url":"https://pith.science/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/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":"2026-06-20T11:04:33Z","links":{"resolver":"https://pith.science/pith/SDX6QQA7OPKQBXIXX4CZCAORK3","bundle":"https://pith.science/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/bundle.json","state":"https://pith.science/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDX6QQA7OPKQBXIXX4CZCAORK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SDX6QQA7OPKQBXIXX4CZCAORK3","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":"8df9a50f42860691cb553b11e93ab8210c14d49ddd42fdc68c09b321dd8b0ad7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T18:47:52Z","title_canon_sha256":"2644b8c6be61f7d9e7cce3996648b962e471a4f17559d6ea57fc508e76bf7a1a"},"schema_version":"1.0","source":{"id":"1602.06887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06887","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06887v1","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06887","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"SDX6QQA7OPKQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDX6QQA7OPKQBXIX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDX6QQA7","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:ae8cc466885a08d9c78228302506fd9c55ec71e5a54edb9bf2e1e87ce0a56cd4","target":"graph","created_at":"2026-05-18T00:34:23Z","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":"VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by considering the complex of cochains which are k-homogeneous on the linear fiber. Our main result is a Van Est theorem for such cochains. We also work out two applications to the general theory of representations of Lie groupoids and algebroids. The case k=1 yields a Van Est map for representations up to homotopy on 2-term graded vector bundles. Arbitrary k-homogeneous cochains on suitable VB-groupoids lead to a novel ","authors_text":"Alejandro Cabrera, Thiago Drummond","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T18:47:52Z","title":"Van Est isomorphism for homogeneous cochains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06887","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":"sha256:59ddace6d864a5fa51d59207338522700ce911579709acd7ee39830509917bab","target":"record","created_at":"2026-05-18T00:34:23Z","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":"8df9a50f42860691cb553b11e93ab8210c14d49ddd42fdc68c09b321dd8b0ad7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T18:47:52Z","title_canon_sha256":"2644b8c6be61f7d9e7cce3996648b962e471a4f17559d6ea57fc508e76bf7a1a"},"schema_version":"1.0","source":{"id":"1602.06887","kind":"arxiv","version":1}},"canonical_sha256":"90efe8401f73d500dd17bf059101d156e64cd6ca7cd09027a4550653ba7f5399","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90efe8401f73d500dd17bf059101d156e64cd6ca7cd09027a4550653ba7f5399","first_computed_at":"2026-05-18T00:34:23.232360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:23.232360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwgUR6C0fGd/pmUd0VSYCTwna+/ElIJpr6XtAsj7bgP8ZLUiyO90guRwcPhiwxvG7q3P2wD77FWMWJFMiIJIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:23.232841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59ddace6d864a5fa51d59207338522700ce911579709acd7ee39830509917bab","sha256:ae8cc466885a08d9c78228302506fd9c55ec71e5a54edb9bf2e1e87ce0a56cd4"],"state_sha256":"ea66712719ccc7ffda2aa42b097ae482fd0d14244ca50db7f9e7917ba31d61f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krSPTtSy4TmwADMR1dVPbN7QVY0HyC48F9jGEWfjNGEmvVRzbhb2JzI4RsaQZ+HJ1WNl43gyjLpspPiRmI1iBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:04:33.373765Z","bundle_sha256":"dc5b384162306b70f54c58ede6cbc15f32a1181c8e7501c24d72cfaf9447e4f1"}}