{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QWHG3S2WRQ6QATMP4UJGL2WZUQ","short_pith_number":"pith:QWHG3S2W","schema_version":"1.0","canonical_sha256":"858e6dcb568c3d004d8fe51265ead9a42589daad67096f1ef69248e07b20304a","source":{"kind":"arxiv","id":"0911.4170","version":3},"attestation_state":"computed","paper":{"title":"Isotropy of orthogonal involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Nikita A. Karpenko","submitted_at":"2009-11-21T09:55:23Z","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."},"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":"0911.4170","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-21T09:55:23Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"c1bed45820709411603798b612c3699fba089e771d9620c34f8f6b09b342dd8b","abstract_canon_sha256":"91a98ab5376da4e123ad2acc20897563ba0057b7508b819a0a5950b17c783bf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:55.641625Z","signature_b64":"z2/9DePz/16vmkH4E3/Wa8xX15ziSaAkagDKHiVvdZP2R/qDQZXyFUMzMEZcPXh7N6JTsIdyl9IJeXh/HeZMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"858e6dcb568c3d004d8fe51265ead9a42589daad67096f1ef69248e07b20304a","last_reissued_at":"2026-05-18T04:26:55.641051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:55.641051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isotropy of orthogonal involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Nikita A. Karpenko","submitted_at":"2009-11-21T09:55:23Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4170","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":"0911.4170","created_at":"2026-05-18T04:26:55.641130+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.4170v3","created_at":"2026-05-18T04:26:55.641130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4170","created_at":"2026-05-18T04:26:55.641130+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWHG3S2WRQ6Q","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWHG3S2WRQ6QATMP","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWHG3S2W","created_at":"2026-05-18T12:26:01.383474+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/QWHG3S2WRQ6QATMP4UJGL2WZUQ","json":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ.json","graph_json":"https://pith.science/api/pith-number/QWHG3S2WRQ6QATMP4UJGL2WZUQ/graph.json","events_json":"https://pith.science/api/pith-number/QWHG3S2WRQ6QATMP4UJGL2WZUQ/events.json","paper":"https://pith.science/paper/QWHG3S2W"},"agent_actions":{"view_html":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ","download_json":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ.json","view_paper":"https://pith.science/paper/QWHG3S2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.4170&json=true","fetch_graph":"https://pith.science/api/pith-number/QWHG3S2WRQ6QATMP4UJGL2WZUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QWHG3S2WRQ6QATMP4UJGL2WZUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ/action/storage_attestation","attest_author":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ/action/author_attestation","sign_citation":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ/action/citation_signature","submit_replication":"https://pith.science/pith/QWHG3S2WRQ6QATMP4UJGL2WZUQ/action/replication_record"}},"created_at":"2026-05-18T04:26:55.641130+00:00","updated_at":"2026-05-18T04:26:55.641130+00:00"}