{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QXXPH7KKSSBQPYFSKG6EXD4UUQ","short_pith_number":"pith:QXXPH7KK","schema_version":"1.0","canonical_sha256":"85eef3fd4a948307e0b251bc4b8f94a407622071d186ca0695d7d1ac6a1066cf","source":{"kind":"arxiv","id":"1312.0247","version":1},"attestation_state":"computed","paper":{"title":"Vector bundles from generalized pairs of cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Chao You, Vladimir Manuilov","submitted_at":"2013-12-01T16:51:44Z","abstract_excerpt":"It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still determine vector bundles."},"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":"1312.0247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-12-01T16:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"4eb1954f9e8a0c335ba2aab54aee254c098ed0181efec3a9988068a3458b56a8","abstract_canon_sha256":"40f9a2b6aae48bc8d7b30e77fb89928c9818d30911ce5758598cc9c3447735a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.269221Z","signature_b64":"DWAC+mel4nfEIYvExgTsQ0t2ZZkJhjBk+VsuahfNWuEooHmN/eLqSSITTqTx/vGnB2UMmrFHHFgQAg5uF3wfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85eef3fd4a948307e0b251bc4b8f94a407622071d186ca0695d7d1ac6a1066cf","last_reissued_at":"2026-05-18T03:05:46.268496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.268496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector bundles from generalized pairs of cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Chao You, Vladimir Manuilov","submitted_at":"2013-12-01T16:51:44Z","abstract_excerpt":"It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still determine vector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0247","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":"1312.0247","created_at":"2026-05-18T03:05:46.268616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0247v1","created_at":"2026-05-18T03:05:46.268616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0247","created_at":"2026-05-18T03:05:46.268616+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXXPH7KKSSBQ","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXXPH7KKSSBQPYFS","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXXPH7KK","created_at":"2026-05-18T12:27:57.521954+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/QXXPH7KKSSBQPYFSKG6EXD4UUQ","json":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ.json","graph_json":"https://pith.science/api/pith-number/QXXPH7KKSSBQPYFSKG6EXD4UUQ/graph.json","events_json":"https://pith.science/api/pith-number/QXXPH7KKSSBQPYFSKG6EXD4UUQ/events.json","paper":"https://pith.science/paper/QXXPH7KK"},"agent_actions":{"view_html":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ","download_json":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ.json","view_paper":"https://pith.science/paper/QXXPH7KK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0247&json=true","fetch_graph":"https://pith.science/api/pith-number/QXXPH7KKSSBQPYFSKG6EXD4UUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QXXPH7KKSSBQPYFSKG6EXD4UUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ/action/storage_attestation","attest_author":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ/action/author_attestation","sign_citation":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ/action/citation_signature","submit_replication":"https://pith.science/pith/QXXPH7KKSSBQPYFSKG6EXD4UUQ/action/replication_record"}},"created_at":"2026-05-18T03:05:46.268616+00:00","updated_at":"2026-05-18T03:05:46.268616+00:00"}