{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:3IDTT33TGPL3XPDYRETMXESZLM","short_pith_number":"pith:3IDTT33T","schema_version":"1.0","canonical_sha256":"da0739ef7333d7bbbc788926cb92595b2bd50382e21f881949bd21b811916412","source":{"kind":"arxiv","id":"0905.1423","version":3},"attestation_state":"computed","paper":{"title":"On Grothendieck--Serre's conjecture concerning principal G-bundles over reductive group schemes:II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"I. Panin","submitted_at":"2009-05-09T18:27:27Z","abstract_excerpt":"A proof of Grothendieck--Serre conjecture on principal bundles over a semi-local regular ring containing an infinite field is given in [FP] recently. That proof is based significantly on Theorem 1.0.1 stated below in the Introduction and proven in the present preprint. Theorem 1.0.1 itself is a consequence of two purity theorems (Theorems A and 10.0.30) proven below in the present preprint. The geometric part of a new preprint [PSV] and the main result of an article [C-T-S] are used significantly in proofs of those two purity theorems.\n  One of that purity result looks as follows. Let O be a s"},"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":"0905.1423","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-09T18:27:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"16fe26420f4d603d8fc3edb883c1c5c3c7a48cae95b9e085403b2e66fe69a226","abstract_canon_sha256":"bee5fd24a8f0eb66b59e9c22b61f3ac14f2a28eb7b08c4d1a94088a823c7b97c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:10.491763Z","signature_b64":"8+RXe3xUbY7ATjRP//2vBNtGkl3S6nfdy9lELYkYIIWDou5MFYpBhtN0rRmkODMazUpnuu6qEdGA5fc+uPJ3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da0739ef7333d7bbbc788926cb92595b2bd50382e21f881949bd21b811916412","last_reissued_at":"2026-05-18T03:27:10.491058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:10.491058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Grothendieck--Serre's conjecture concerning principal G-bundles over reductive group schemes:II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"I. Panin","submitted_at":"2009-05-09T18:27:27Z","abstract_excerpt":"A proof of Grothendieck--Serre conjecture on principal bundles over a semi-local regular ring containing an infinite field is given in [FP] recently. That proof is based significantly on Theorem 1.0.1 stated below in the Introduction and proven in the present preprint. Theorem 1.0.1 itself is a consequence of two purity theorems (Theorems A and 10.0.30) proven below in the present preprint. The geometric part of a new preprint [PSV] and the main result of an article [C-T-S] are used significantly in proofs of those two purity theorems.\n  One of that purity result looks as follows. Let O be a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1423","kind":"arxiv","version":3},"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":"0905.1423","created_at":"2026-05-18T03:27:10.491155+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.1423v3","created_at":"2026-05-18T03:27:10.491155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1423","created_at":"2026-05-18T03:27:10.491155+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IDTT33TGPL3","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IDTT33TGPL3XPDY","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IDTT33T","created_at":"2026-05-18T12:25:58.018023+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/3IDTT33TGPL3XPDYRETMXESZLM","json":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM.json","graph_json":"https://pith.science/api/pith-number/3IDTT33TGPL3XPDYRETMXESZLM/graph.json","events_json":"https://pith.science/api/pith-number/3IDTT33TGPL3XPDYRETMXESZLM/events.json","paper":"https://pith.science/paper/3IDTT33T"},"agent_actions":{"view_html":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM","download_json":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM.json","view_paper":"https://pith.science/paper/3IDTT33T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.1423&json=true","fetch_graph":"https://pith.science/api/pith-number/3IDTT33TGPL3XPDYRETMXESZLM/graph.json","fetch_events":"https://pith.science/api/pith-number/3IDTT33TGPL3XPDYRETMXESZLM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM/action/storage_attestation","attest_author":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM/action/author_attestation","sign_citation":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM/action/citation_signature","submit_replication":"https://pith.science/pith/3IDTT33TGPL3XPDYRETMXESZLM/action/replication_record"}},"created_at":"2026-05-18T03:27:10.491155+00:00","updated_at":"2026-05-18T03:27:10.491155+00:00"}