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Jagy conjectured that if $n$ is square free and the number of spinor genera in the genus of $f$ equals to the number of spinor genera in the genus of $g$, then such a genus-correspondence respects spinor genus in the sense that for any representable pairs $(f,g), (f',"},"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":"1609.03031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-10T11:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"3588fdf608bdce49f024c14bdfa2ed1d8cdd633bc2c31bf8fbd4f59bf4c7ac6b","abstract_canon_sha256":"a3174e1f87b1d833065a8c593b3782d4318ac405655b6e673ba98f3c0fc51abf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.099077Z","signature_b64":"FeUtDkgW0rUVePWgBGuIIr4fCbWt/hOQobBS7SIoE0Mepm6zsTHncZF4SzuT4A17fxZsqR0anED2N2rpVV+aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"132a48fe78894f809bb7907dd7e7cc61d381d92567674b4d4e78d4900cd803f3","last_reissued_at":"2026-05-18T01:04:49.098497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.098497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Genus-correspondences respecting spinor genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Byeong-Kweon Oh, Jangwon Ju","submitted_at":"2016-09-10T11:39:36Z","abstract_excerpt":"For two positive definite integral ternary quadratic forms $f$ and $g$ and a positive integer $n$, if $n\\cdot g$ is represented by $f$ and $n\\cdot dg=df$, then the pair $(f,g)$ is called a representable pair by scaling $n$. 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