{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UFJG6OOIKE3FNWYPM4TNL5JECD","short_pith_number":"pith:UFJG6OOI","schema_version":"1.0","canonical_sha256":"a1526f39c8513656db0f6726d5f52410c4752f14fbafaef0fd2149589d2b3d45","source":{"kind":"arxiv","id":"1809.03965","version":2},"attestation_state":"computed","paper":{"title":"The descent of biquaternion algebras in characteristic two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Chapman, Ahmed Laghribi, Demba Barry","submitted_at":"2018-09-11T15:15:11Z","abstract_excerpt":"In this paper we associate an invariant to a biquaternion algebra $B$ over a field $K$ with a subfield $F$ such that $K/F$ is a quadratic separable extension and $\\operatorname{char}(F)=2$. We show that this invariant is trivial exactly when $B \\cong B_0 \\otimes K$ for some biquaternion algebra $B_0$ over $F$. We also study the behavior of this invariant under certain field extensions and provide several interesting examples."},"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":"1809.03965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-11T15:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"c51c28c0972feb5cccbec750fcfe411463495781f95202be1c811e80fd9b4101","abstract_canon_sha256":"d50b83900466438db9da299f3c2dc94b0fc6d7156a34cfb6cb18cfd6d581466b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:05.205976Z","signature_b64":"spdVXLgTr/ZA3t9MNZ4GSnZR48H1lahdjT2sO3mRNN3R+WNBDsAC40MNrC0P9DS/Wa9M1dMPMSHpurR2oeh2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1526f39c8513656db0f6726d5f52410c4752f14fbafaef0fd2149589d2b3d45","last_reissued_at":"2026-05-17T23:52:05.205566Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:05.205566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The descent of biquaternion algebras in characteristic two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Chapman, Ahmed Laghribi, Demba Barry","submitted_at":"2018-09-11T15:15:11Z","abstract_excerpt":"In this paper we associate an invariant to a biquaternion algebra $B$ over a field $K$ with a subfield $F$ such that $K/F$ is a quadratic separable extension and $\\operatorname{char}(F)=2$. We show that this invariant is trivial exactly when $B \\cong B_0 \\otimes K$ for some biquaternion algebra $B_0$ over $F$. We also study the behavior of this invariant under certain field extensions and provide several interesting examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03965","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":"1809.03965","created_at":"2026-05-17T23:52:05.205627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03965v2","created_at":"2026-05-17T23:52:05.205627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03965","created_at":"2026-05-17T23:52:05.205627+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFJG6OOIKE3F","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFJG6OOIKE3FNWYP","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFJG6OOI","created_at":"2026-05-18T12:32:56.356000+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/UFJG6OOIKE3FNWYPM4TNL5JECD","json":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD.json","graph_json":"https://pith.science/api/pith-number/UFJG6OOIKE3FNWYPM4TNL5JECD/graph.json","events_json":"https://pith.science/api/pith-number/UFJG6OOIKE3FNWYPM4TNL5JECD/events.json","paper":"https://pith.science/paper/UFJG6OOI"},"agent_actions":{"view_html":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD","download_json":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD.json","view_paper":"https://pith.science/paper/UFJG6OOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03965&json=true","fetch_graph":"https://pith.science/api/pith-number/UFJG6OOIKE3FNWYPM4TNL5JECD/graph.json","fetch_events":"https://pith.science/api/pith-number/UFJG6OOIKE3FNWYPM4TNL5JECD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD/action/storage_attestation","attest_author":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD/action/author_attestation","sign_citation":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD/action/citation_signature","submit_replication":"https://pith.science/pith/UFJG6OOIKE3FNWYPM4TNL5JECD/action/replication_record"}},"created_at":"2026-05-17T23:52:05.205627+00:00","updated_at":"2026-05-17T23:52:05.205627+00:00"}