{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UNGRC53N3CKJBWJB56WFQ5Q4JT","short_pith_number":"pith:UNGRC53N","schema_version":"1.0","canonical_sha256":"a34d11776dd89490d921efac58761c4cea9ca766af1824029fcd9a0b5935b8dd","source":{"kind":"arxiv","id":"1308.3078","version":4},"attestation_state":"computed","paper":{"title":"Affine Grassmannians of group schemes and exotic principal bundles over A^1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roman Fedorov","submitted_at":"2013-08-14T10:18:57Z","abstract_excerpt":"Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this end we define affine Grassmannians for group schemes and study their Bruhat decompositions for semi-simple group schemes. We also give examples of principal G-bundles over A^1_U with split G such that the bundles are not isomorphic to pull-backs from U."},"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":"1308.3078","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-14T10:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"fb948c75d3ceb6a68b0e2984a1609a55fd851d984cdac1c92d3eb27cab18142b","abstract_canon_sha256":"2f06493c336811d94daf2bc1c0d72e1860644faa4b81b5c94e1344cc6daa6b2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:28.249216Z","signature_b64":"ybKf0jujntgwbZhFs9USDOoug2/+M+U0yiSupVOGwwltjuBfXB49vSm8l7OovQkpMBC7C9iLKvkrI3sMeQM2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a34d11776dd89490d921efac58761c4cea9ca766af1824029fcd9a0b5935b8dd","last_reissued_at":"2026-05-18T00:59:28.248659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:28.248659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine Grassmannians of group schemes and exotic principal bundles over A^1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roman Fedorov","submitted_at":"2013-08-14T10:18:57Z","abstract_excerpt":"Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this end we define affine Grassmannians for group schemes and study their Bruhat decompositions for semi-simple group schemes. We also give examples of principal G-bundles over A^1_U with split G such that the bundles are not isomorphic to pull-backs from U."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3078","kind":"arxiv","version":4},"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":"1308.3078","created_at":"2026-05-18T00:59:28.248740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3078v4","created_at":"2026-05-18T00:59:28.248740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3078","created_at":"2026-05-18T00:59:28.248740+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNGRC53N3CKJ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNGRC53N3CKJBWJB","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNGRC53N","created_at":"2026-05-18T12:28:02.375192+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/UNGRC53N3CKJBWJB56WFQ5Q4JT","json":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT.json","graph_json":"https://pith.science/api/pith-number/UNGRC53N3CKJBWJB56WFQ5Q4JT/graph.json","events_json":"https://pith.science/api/pith-number/UNGRC53N3CKJBWJB56WFQ5Q4JT/events.json","paper":"https://pith.science/paper/UNGRC53N"},"agent_actions":{"view_html":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT","download_json":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT.json","view_paper":"https://pith.science/paper/UNGRC53N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3078&json=true","fetch_graph":"https://pith.science/api/pith-number/UNGRC53N3CKJBWJB56WFQ5Q4JT/graph.json","fetch_events":"https://pith.science/api/pith-number/UNGRC53N3CKJBWJB56WFQ5Q4JT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT/action/storage_attestation","attest_author":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT/action/author_attestation","sign_citation":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT/action/citation_signature","submit_replication":"https://pith.science/pith/UNGRC53N3CKJBWJB56WFQ5Q4JT/action/replication_record"}},"created_at":"2026-05-18T00:59:28.248740+00:00","updated_at":"2026-05-18T00:59:28.248740+00:00"}