{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F5OJNRJ5K6VMUP7O2NAVALORHH","short_pith_number":"pith:F5OJNRJ5","schema_version":"1.0","canonical_sha256":"2f5c96c53d57aaca3feed341502dd139ea5e0ca97f181583ccc05f443ccc8a80","source":{"kind":"arxiv","id":"1312.1676","version":6},"attestation_state":"computed","paper":{"title":"Chain Equivalences for Symplectic Bases, Quadratic Forms and Tensor Products of Quaternion Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adam Chapman","submitted_at":"2013-12-05T20:41:08Z","abstract_excerpt":"We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field."},"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":"1312.1676","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-05T20:41:08Z","cross_cats_sorted":[],"title_canon_sha256":"7a1e4ec27617936101ea11f2cb162a7155c0f24b32229f4c538210ced3400a2a","abstract_canon_sha256":"b25ca8abb3bf8cecfc0e9fcf9ca7afb8fba553c459d33557ffe47af1e523fa98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:11.239436Z","signature_b64":"IvzE6/dQv1nyyYqyt4NxXy980u2zRdJwPL46sq2XcMfeqaZiDKkGOyQ68cGcjgwrHAEfgW6bnzzwIPz6xWdCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f5c96c53d57aaca3feed341502dd139ea5e0ca97f181583ccc05f443ccc8a80","last_reissued_at":"2026-05-18T02:29:11.238773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:11.238773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chain Equivalences for Symplectic Bases, Quadratic Forms and Tensor Products of Quaternion Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adam Chapman","submitted_at":"2013-12-05T20:41:08Z","abstract_excerpt":"We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1676","kind":"arxiv","version":6},"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":"1312.1676","created_at":"2026-05-18T02:29:11.238873+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1676v6","created_at":"2026-05-18T02:29:11.238873+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1676","created_at":"2026-05-18T02:29:11.238873+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5OJNRJ5K6VM","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5OJNRJ5K6VMUP7O","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5OJNRJ5","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/F5OJNRJ5K6VMUP7O2NAVALORHH","json":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH.json","graph_json":"https://pith.science/api/pith-number/F5OJNRJ5K6VMUP7O2NAVALORHH/graph.json","events_json":"https://pith.science/api/pith-number/F5OJNRJ5K6VMUP7O2NAVALORHH/events.json","paper":"https://pith.science/paper/F5OJNRJ5"},"agent_actions":{"view_html":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH","download_json":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH.json","view_paper":"https://pith.science/paper/F5OJNRJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1676&json=true","fetch_graph":"https://pith.science/api/pith-number/F5OJNRJ5K6VMUP7O2NAVALORHH/graph.json","fetch_events":"https://pith.science/api/pith-number/F5OJNRJ5K6VMUP7O2NAVALORHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH/action/storage_attestation","attest_author":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH/action/author_attestation","sign_citation":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH/action/citation_signature","submit_replication":"https://pith.science/pith/F5OJNRJ5K6VMUP7O2NAVALORHH/action/replication_record"}},"created_at":"2026-05-18T02:29:11.238873+00:00","updated_at":"2026-05-18T02:29:11.238873+00:00"}