{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QWHG3S2WRQ6QATMP4UJGL2WZUQ","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":"91a98ab5376da4e123ad2acc20897563ba0057b7508b819a0a5950b17c783bf4","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-21T09:55:23Z","title_canon_sha256":"c1bed45820709411603798b612c3699fba089e771d9620c34f8f6b09b342dd8b"},"schema_version":"1.0","source":{"id":"0911.4170","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4170","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4170v3","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4170","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"pith_short_12","alias_value":"QWHG3S2WRQ6Q","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QWHG3S2WRQ6QATMP","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QWHG3S2W","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:10c6bf41ccdde5b6422faf88a5ee1c89e01b771aa40fdefd7fc5e36ecb7b7be8","target":"graph","created_at":"2026-05-18T04:26:55Z","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":"An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is not 2). The proof makes use of a structure theorem for Chow motives with finite coefficients of projective homogeneous varieties, of incompressibility of certain generalized Severi-Brauer varieties, and of Steenrod operations.","authors_text":"Nikita A. Karpenko","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-21T09:55:23Z","title":"Isotropy of orthogonal involutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4170","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:a03080116068f7395d86b4f1819389bc9c4a3d92c62b40aec233e25c7762a7d6","target":"record","created_at":"2026-05-18T04:26:55Z","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":"91a98ab5376da4e123ad2acc20897563ba0057b7508b819a0a5950b17c783bf4","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-21T09:55:23Z","title_canon_sha256":"c1bed45820709411603798b612c3699fba089e771d9620c34f8f6b09b342dd8b"},"schema_version":"1.0","source":{"id":"0911.4170","kind":"arxiv","version":3}},"canonical_sha256":"858e6dcb568c3d004d8fe51265ead9a42589daad67096f1ef69248e07b20304a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"858e6dcb568c3d004d8fe51265ead9a42589daad67096f1ef69248e07b20304a","first_computed_at":"2026-05-18T04:26:55.641051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:55.641051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2/9DePz/16vmkH4E3/Wa8xX15ziSaAkagDKHiVvdZP2R/qDQZXyFUMzMEZcPXh7N6JTsIdyl9IJeXh/HeZMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:55.641625Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4170","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a03080116068f7395d86b4f1819389bc9c4a3d92c62b40aec233e25c7762a7d6","sha256:10c6bf41ccdde5b6422faf88a5ee1c89e01b771aa40fdefd7fc5e36ecb7b7be8"],"state_sha256":"31f21bdffc206f3aa406cfc0dad16f642ed236605a675425b086c527d0463008"}