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Some properties of the involution, such as hyperbolicity, and isotropy up to an odd-degree extension of the base field, are encoded in this quadratic form, meaning that they hold for the involution $\\sigma$ if and only if they hold for $q_\\sigma$. As opposed to this, we prove that there exists non-totally decomposable"},"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":"1807.07045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-18T17:18:49Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"4a25944a77a4af26c3482c0f2f1967757d9a6d77e334b5ad60e8a542a04d5e23","abstract_canon_sha256":"449997fac8678454310591458f49078ea5a2c7b9dd06ca3385ac91610bc2e347"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:24.999368Z","signature_b64":"Yq0f4hSYzHRdDRnfwf0LrMbPr8+030TJytNtgN0RjANDCsMYSUh7hCVGeJPelIHGaz7IC0TKyf39QALx35qOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43e37e054cbce96a4165513a7b4bc5fb56105c3f47f687dc01a04ad74c9b2282","last_reissued_at":"2026-05-18T00:10:24.998587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:24.998587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.GR","authors_text":"Anne Qu\\'eguiner-Mathieu, Jean-Pierre Tignol","submitted_at":"2018-07-18T17:18:49Z","abstract_excerpt":"An orthogonal involution $\\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\\sigma$ over $\\mathcal{F}(A)$, which is uniquely defined up to a scalar factor. Some properties of the involution, such as hyperbolicity, and isotropy up to an odd-degree extension of the base field, are encoded in this quadratic form, meaning that they hold for the involution $\\sigma$ if and only if they hold for $q_\\sigma$. 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