{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7OJUKKBHJP635YRQT3QFUXT4D6","short_pith_number":"pith:7OJUKKBH","canonical_record":{"source":{"id":"1406.0247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"0eb559d44796a0c7debf1d9546fc989960770764376202c8983dc4e7df37cd6f","abstract_canon_sha256":"888d7ab68c36b01b9005751a034ca5538250049adf6f049a82280dc50e2419b1"},"schema_version":"1.0"},"canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","source":{"kind":"arxiv","id":"1406.0247","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0247","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0247v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0247","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"7OJUKKBHJP63","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7OJUKKBHJP635YRQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7OJUKKBH","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7OJUKKBHJP635YRQT3QFUXT4D6","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"0eb559d44796a0c7debf1d9546fc989960770764376202c8983dc4e7df37cd6f","abstract_canon_sha256":"888d7ab68c36b01b9005751a034ca5538250049adf6f049a82280dc50e2419b1"},"schema_version":"1.0"},"canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.377376Z","signature_b64":"SDL0bdyDbVJYPZ5RB5Zu6Dp2Ql/u59m7iCfJZC1w7CPVkNVB+k1wVGYOyM80rE5o227PLOdy0TEYiXz77Sd4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","last_reissued_at":"2026-05-18T02:50:41.376675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.376675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0247","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmX5NYm1kkDa7nUxvluU3HOB/M5Mv5GdjbQkPH1cONBQEjTutYf0czqxTUsaIu8zIy8D0EAYdLBtZyGZzRoNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T03:41:38.038748Z"},"content_sha256":"1c539ee06137903b7a38589adb7c319a0335a533fac3807e5ae42c628d3cd69c","schema_version":"1.0","event_id":"sha256:1c539ee06137903b7a38589adb7c319a0335a533fac3807e5ae42c628d3cd69c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7OJUKKBHJP635YRQT3QFUXT4D6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of Grothendieck--Serre conjecture on principal G-bundles over regular local rings containing a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Panin","submitted_at":"2014-06-02T05:16:05Z","abstract_excerpt":"Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of pointed sets H^1_{et}(R,G) \\to H^1_{et}(K,G), induced by the inclusion of R into K, has a trivial kernel. Certain arguments used in the present preprint do not work if the ring R contains a characteristic zero field. In that case and, more generally, in the case when the regular local ring R contains an infinite field this result is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0247","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMPucsLKjGy8LbMlNWqMnrJVY70ZN8qeNCJ2kAHGwyqGipPm8mSqQiJNUt2VE78gmdmMEgILf8B/S9ySzps1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T03:41:38.039092Z"},"content_sha256":"fee97294c55596342cbe77d585213aaac5105b0d35851b745263270b7550746d","schema_version":"1.0","event_id":"sha256:fee97294c55596342cbe77d585213aaac5105b0d35851b745263270b7550746d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/bundle.json","state_url":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OJUKKBHJP635YRQT3QFUXT4D6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T03:41:38Z","links":{"resolver":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6","bundle":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/bundle.json","state":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OJUKKBHJP635YRQT3QFUXT4D6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7OJUKKBHJP635YRQT3QFUXT4D6","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":"888d7ab68c36b01b9005751a034ca5538250049adf6f049a82280dc50e2419b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","title_canon_sha256":"0eb559d44796a0c7debf1d9546fc989960770764376202c8983dc4e7df37cd6f"},"schema_version":"1.0","source":{"id":"1406.0247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0247","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0247v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0247","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"7OJUKKBHJP63","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7OJUKKBHJP635YRQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7OJUKKBH","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:fee97294c55596342cbe77d585213aaac5105b0d35851b745263270b7550746d","target":"graph","created_at":"2026-05-18T02:50:41Z","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":"Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of pointed sets H^1_{et}(R,G) \\to H^1_{et}(K,G), induced by the inclusion of R into K, has a trivial kernel. Certain arguments used in the present preprint do not work if the ring R contains a characteristic zero field. In that case and, more generally, in the case when the regular local ring R contains an infinite field this result is","authors_text":"Ivan Panin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","title":"Proof of Grothendieck--Serre conjecture on principal G-bundles over regular local rings containing a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0247","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":"sha256:1c539ee06137903b7a38589adb7c319a0335a533fac3807e5ae42c628d3cd69c","target":"record","created_at":"2026-05-18T02:50:41Z","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":"888d7ab68c36b01b9005751a034ca5538250049adf6f049a82280dc50e2419b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","title_canon_sha256":"0eb559d44796a0c7debf1d9546fc989960770764376202c8983dc4e7df37cd6f"},"schema_version":"1.0","source":{"id":"1406.0247","kind":"arxiv","version":1}},"canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","first_computed_at":"2026-05-18T02:50:41.376675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:41.376675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDL0bdyDbVJYPZ5RB5Zu6Dp2Ql/u59m7iCfJZC1w7CPVkNVB+k1wVGYOyM80rE5o227PLOdy0TEYiXz77Sd4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:41.377376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c539ee06137903b7a38589adb7c319a0335a533fac3807e5ae42c628d3cd69c","sha256:fee97294c55596342cbe77d585213aaac5105b0d35851b745263270b7550746d"],"state_sha256":"fdae1a7df6f90f5e54cbc2f01379a83e724d7571f017b1e9b54e7bf80e92e874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hd1lFgUAHQK3c1MtTP/M73wIi0BDhUw5dquYiU3irxkhNYt7CsOCaTSX1V8IwJlDzox22B35aBeqKuXXL2xABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T03:41:38.041868Z","bundle_sha256":"7dd6001aab5d99de4587d90d1893fa4056364305f0bf68b7329fa4469f8f003d"}}