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Raf Bocklandt proved that if $TV/(R)$ is 3-Calabi-Yau, then it is isomorphic to $J({\\sf{w}})$, the \"Jacobian algebra\" of some ${\\sf{w}} \\in V^{\\otimes 3}$. This paper classifies the ${\\sf{w}}\\in V^{\\otimes 3}$ such that $J({\\sf{w}})$ is 3-Calabi-Yau. The classification depends on how ${\\sf{w}}$ transforms under the action of the symmetric group $S_3$ "},"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":"1502.07403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-25T23:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"0f67bb6fa59699b434135aabe5161ccf3e5104a18b6b2424a113ca089474b672","abstract_canon_sha256":"08c0784ac98f7063e0962776e5a3409d7b49920fbe89540634aac8d77a68a0b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:42.289117Z","signature_b64":"sw4xolQNLmu3Jq7lzYBc7CaFTcJFtvhc+qWvT65y9xm9wwfSKIu4X+pPrjNRywAZMNPx9dtHsgoWpMjiljZbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a8cb4b95f7a9e5420ecb4d722e19c62399e0efd1219b269552c5f1d212d170d","last_reissued_at":"2026-05-18T01:09:42.288526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:42.288526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Classification of 3-Calabi-Yau algebras with 3 generators and 3 quadratic relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Izuru Mori, S. 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