{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EBKELYMY54VHKCTW7HRKUEZ26J","short_pith_number":"pith:EBKELYMY","schema_version":"1.0","canonical_sha256":"205445e198ef2a750a76f9e2aa133af25a0b7f457dd93777da0b7c60328ccdff","source":{"kind":"arxiv","id":"1310.1505","version":2},"attestation_state":"computed","paper":{"title":"Involutions, odd-degree extensions and generic splitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anne Qu\\'eguiner-Mathieu, Jodi Black","submitted_at":"2013-10-05T18:22:04Z","abstract_excerpt":"Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two quadratic forms $q, q^\\prime$ over $F$, if $q_L \\cong q^\\prime_L$ then $q \\cong q^\\prime$. It is natural to ask whether similar results hold for algebras with involution. We give a survey of the progress on these three questions with particular attention to the relevance of hyperbolicity, isotropy and isomorphism over some {appropriate} function field. Incidentally,"},"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":"1310.1505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-05T18:22:04Z","cross_cats_sorted":[],"title_canon_sha256":"3d1f953fcfb55edcdeeb1532f3ae4b9767a2ec863918f48013ad3d9bca8777cd","abstract_canon_sha256":"5787325ae53763b4ad025912ce4e76371d7c6a6bacc31cc48f44013b831dd3db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:26.048125Z","signature_b64":"MFsD2YEj6IsNtduc2izLVsvJWJ8etACQ+LP1DT+cX8Sarm92lMzuijfhfru9M6tEUYjgTk8K+t5iL+2LopF9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"205445e198ef2a750a76f9e2aa133af25a0b7f457dd93777da0b7c60328ccdff","last_reissued_at":"2026-05-18T02:48:26.047752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:26.047752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Involutions, odd-degree extensions and generic splitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anne Qu\\'eguiner-Mathieu, Jodi Black","submitted_at":"2013-10-05T18:22:04Z","abstract_excerpt":"Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two quadratic forms $q, q^\\prime$ over $F$, if $q_L \\cong q^\\prime_L$ then $q \\cong q^\\prime$. It is natural to ask whether similar results hold for algebras with involution. We give a survey of the progress on these three questions with particular attention to the relevance of hyperbolicity, isotropy and isomorphism over some {appropriate} function field. Incidentally,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1505","kind":"arxiv","version":2},"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":"1310.1505","created_at":"2026-05-18T02:48:26.047806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.1505v2","created_at":"2026-05-18T02:48:26.047806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1505","created_at":"2026-05-18T02:48:26.047806+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBKELYMY54VH","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBKELYMY54VHKCTW","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBKELYMY","created_at":"2026-05-18T12:27:43.054852+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/EBKELYMY54VHKCTW7HRKUEZ26J","json":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J.json","graph_json":"https://pith.science/api/pith-number/EBKELYMY54VHKCTW7HRKUEZ26J/graph.json","events_json":"https://pith.science/api/pith-number/EBKELYMY54VHKCTW7HRKUEZ26J/events.json","paper":"https://pith.science/paper/EBKELYMY"},"agent_actions":{"view_html":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J","download_json":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J.json","view_paper":"https://pith.science/paper/EBKELYMY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.1505&json=true","fetch_graph":"https://pith.science/api/pith-number/EBKELYMY54VHKCTW7HRKUEZ26J/graph.json","fetch_events":"https://pith.science/api/pith-number/EBKELYMY54VHKCTW7HRKUEZ26J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J/action/storage_attestation","attest_author":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J/action/author_attestation","sign_citation":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J/action/citation_signature","submit_replication":"https://pith.science/pith/EBKELYMY54VHKCTW7HRKUEZ26J/action/replication_record"}},"created_at":"2026-05-18T02:48:26.047806+00:00","updated_at":"2026-05-18T02:48:26.047806+00:00"}