{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GMRPKCNMS4MLEQSBEKB4PVCJG2","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":"d8bdbc9ef39edcb72a302da9f3aff86562d5d35423c126a4c7616bbe80ae54df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T07:27:39Z","title_canon_sha256":"e514b86de5702f3342e29f6bfa3865a6534ceb22ff8e649dd9f8c3ddcfee912b"},"schema_version":"1.0","source":{"id":"1707.01763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01763","created_at":"2026-05-18T00:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01763v1","created_at":"2026-05-18T00:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01763","created_at":"2026-05-18T00:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"GMRPKCNMS4ML","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GMRPKCNMS4MLEQSB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GMRPKCNM","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:bca2006da3cdf534b6fbbcf411e3b073ccd1dff34393056a4f73453f93c21868","target":"graph","created_at":"2026-05-18T00:40:47Z","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":"In a series of papers [Pan0], [Pan1], [Pan2], [Pan3] we give a detailed and better structured proof of the Grothendieck--Serre's conjecture for semi-local regular rings containing a finite field. The outline of the proof is the same as in [P1],[P2],[P3]. If the semi-local regular ring contains an infinite field, then the conjecture is proved in [FP]. Thus the conjecture is true for regular local rings containing a field.\n  A proof of Grothendieck--Serre conjecture on principal bundles over a semi-local regular ring containing an arbitrary field is given in [Pan3]. That proof is heavily based o","authors_text":"Ivan Panin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T07:27:39Z","title":"Two purity theorems and the Grothendieck--Serre's conjecture concerning principal G-bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01763","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:c1ab7f0150631356a419944797f2408b5f7cef0e9837cb3bc3623616dd31df99","target":"record","created_at":"2026-05-18T00:40:47Z","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":"d8bdbc9ef39edcb72a302da9f3aff86562d5d35423c126a4c7616bbe80ae54df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T07:27:39Z","title_canon_sha256":"e514b86de5702f3342e29f6bfa3865a6534ceb22ff8e649dd9f8c3ddcfee912b"},"schema_version":"1.0","source":{"id":"1707.01763","kind":"arxiv","version":1}},"canonical_sha256":"3322f509ac9718b242412283c7d44936a31ce66d4baf37d94a35244b13ce9926","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3322f509ac9718b242412283c7d44936a31ce66d4baf37d94a35244b13ce9926","first_computed_at":"2026-05-18T00:40:47.546975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:47.546975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/5kTnchTGS4MfYibxQV6zTyQC/f4MDSYemvpK3slXa5QeWBP6UArkigLeXK7HFnUcRGqF7IsrLet5CpZIZzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:47.547694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1ab7f0150631356a419944797f2408b5f7cef0e9837cb3bc3623616dd31df99","sha256:bca2006da3cdf534b6fbbcf411e3b073ccd1dff34393056a4f73453f93c21868"],"state_sha256":"4368da6bea638b4065ce0ddd5a310a3a11df1ca4193e7ecc905d077e6cebd36b"}