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We use computer algebra to show that every identity for this product in degree $\\le 7$ is a consequence of the three identities in degree $\\le 4$, but that six new identities exist in degree 8. Some but not all of these new identities are noncommutative preimages of the Glennie identity."},"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":"1008.2723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-08-16T17:52:27Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"7d731495ee3093559c73d81db7317241eb6a3eef43ad485fad76229d57494e99","abstract_canon_sha256":"fc546aa0230dd4b1ce01adc7dfccc440fe04c71a132ac780024138cb063fb74b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:12.717036Z","signature_b64":"sRpZa+1ZoTt9PXh1opkbqlmi5MTVyiOY8Kud1nPaksmUJupGG1Jw/sm34y+M1yhwO7GjlTCub8S9ALloVAM7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"708909042677fd161950f97db8e28f0cee53b970f9d28516fb6c8b8d9e4fb306","last_reissued_at":"2026-05-18T04:42:12.716371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:12.716371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special identities for quasi-Jordan algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.RA","authors_text":"Luiz A. Peresi, Murray R. Bremner","submitted_at":"2010-08-16T17:52:27Z","abstract_excerpt":"Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities $a(bc) = a(cb)$, $(ba)a^2 = (ba^2)a$, and $(b,a^2,c) = 2(b,a,c)a$. These identities are satisfied by the product $ab = a \\dashv b + b \\vdash a$ in an associative dialgebra. We use computer algebra to show that every identity for this product in degree $\\le 7$ is a consequence of the three identities in degree $\\le 4$, but that six new identities exist in degree 8. 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