{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR","short_pith_number":"pith:IQNTJ6Z6","schema_version":"1.0","canonical_sha256":"441b34fb3ea9ee54f72a5a3073edce546d84f0689eab2391a04ec01cba0b2bdf","source":{"kind":"arxiv","id":"math/0508534","version":1},"attestation_state":"computed","paper":{"title":"Subcomplexes in Curved BGG-Sequences","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Andreas Cap, Vladimir Soucek","submitted_at":"2005-08-26T12:30:07Z","abstract_excerpt":"BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi-flatness assumptions certain parts of all BGG sequences are complexes.\n  Several examples of structures, including quaternionic structures, hypersurface type CR structures and quaternionic contact structures are discussed in "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0508534","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-08-26T12:30:07Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"07711d247e5c02557f4a095acc9028527580a4d41de93a20aa060c1bacc139e5","abstract_canon_sha256":"25396f322cbb7acaf46298659a5ca0aadfdc17029ac57a32dc5bb6b66f563ac7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:25.211884Z","signature_b64":"xx2VLpcQ5q/P8okSM6fYn6OgPWoxLi+6z+1exHULBmqCUHrlGc7G66Fnr+tVOEAxYOyIPuYjAXtsyZOBJBDUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"441b34fb3ea9ee54f72a5a3073edce546d84f0689eab2391a04ec01cba0b2bdf","last_reissued_at":"2026-05-18T03:48:25.211253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:25.211253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subcomplexes in Curved BGG-Sequences","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Andreas Cap, Vladimir Soucek","submitted_at":"2005-08-26T12:30:07Z","abstract_excerpt":"BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi-flatness assumptions certain parts of all BGG sequences are complexes.\n  Several examples of structures, including quaternionic structures, hypersurface type CR structures and quaternionic contact structures are discussed in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508534","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0508534","created_at":"2026-05-18T03:48:25.211354+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0508534v1","created_at":"2026-05-18T03:48:25.211354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508534","created_at":"2026-05-18T03:48:25.211354+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQNTJ6Z6VHXF","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQNTJ6Z6VHXFJ5ZK","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQNTJ6Z6","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR","json":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR.json","graph_json":"https://pith.science/api/pith-number/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/graph.json","events_json":"https://pith.science/api/pith-number/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/events.json","paper":"https://pith.science/paper/IQNTJ6Z6"},"agent_actions":{"view_html":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR","download_json":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR.json","view_paper":"https://pith.science/paper/IQNTJ6Z6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0508534&json=true","fetch_graph":"https://pith.science/api/pith-number/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/graph.json","fetch_events":"https://pith.science/api/pith-number/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/action/storage_attestation","attest_author":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/action/author_attestation","sign_citation":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/action/citation_signature","submit_replication":"https://pith.science/pith/IQNTJ6Z6VHXFJ5ZKLIYHH3OOKR/action/replication_record"}},"created_at":"2026-05-18T03:48:25.211354+00:00","updated_at":"2026-05-18T03:48:25.211354+00:00"}