{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7QOHVIILBSVJTT3ZKONYL5P54E","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":"813f38b175e88d725b7f79fd73793e5465d0278822574f0e225ed742f588b41c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-26T04:41:30Z","title_canon_sha256":"10549d5de3b6d639cb445f839fd8883ef9481d8492f9b3891fe32144cc8e8976"},"schema_version":"1.0","source":{"id":"2305.16627","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16627","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16627v3","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16627","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"7QOHVIILBSVJ","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_16","alias_value":"7QOHVIILBSVJTT3Z","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_8","alias_value":"7QOHVIIL","created_at":"2026-07-05T09:58:56Z"}],"graph_snapshots":[{"event_id":"sha256:9ab3cdcce0f4b355bba46d574761093986c7644e9423052a0a8f943603468e60","target":"graph","created_at":"2026-07-05T09:58:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.16627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a Noetherian separated scheme. Let $G$ be a reductive $X$-group scheme, and let $E$ be a principal $G$-bundle over $\\mathbb{P}^1_X$. We prove that if the restriction of $E$ to $\\infty\\times X$ is Zariski locally trivial, then $E$ is itself Zariski locally trivial.","authors_text":"Anastasia Stavrova, Ivan Panin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-26T04:41:30Z","title":"On the Gille theorem for the relative projective line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16627","kind":"arxiv","version":3},"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":"sha256:47ca6ca1ccd8284f1a0220661bf8ac5803c8ce1d0c16421f8b5a884d41984d8b","target":"record","created_at":"2026-07-05T09:58:56Z","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":"813f38b175e88d725b7f79fd73793e5465d0278822574f0e225ed742f588b41c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-26T04:41:30Z","title_canon_sha256":"10549d5de3b6d639cb445f839fd8883ef9481d8492f9b3891fe32144cc8e8976"},"schema_version":"1.0","source":{"id":"2305.16627","kind":"arxiv","version":3}},"canonical_sha256":"fc1c7aa10b0caa99cf79539b85f5fde134d2609df7440de34f23b4144d73239e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc1c7aa10b0caa99cf79539b85f5fde134d2609df7440de34f23b4144d73239e","first_computed_at":"2026-07-05T09:58:56.456033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:56.456033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlMg3+EOOI9jiQvJ1T0GiCu0ZhnFgHUNuGT0fsdd4tvc5jDK/QD0GhIGHF6e4j32rVh7POnOb25MvsHhA17eDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:56.456453Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.16627","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47ca6ca1ccd8284f1a0220661bf8ac5803c8ce1d0c16421f8b5a884d41984d8b","sha256:9ab3cdcce0f4b355bba46d574761093986c7644e9423052a0a8f943603468e60"],"state_sha256":"58147e8a9bac918f4e135c30522f0745036265aac6d8c243c0a8bb881c549bc3"}