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Given a quantum pure state $|\\varphi\\rangle\\in \\mathbb{P}(\\mathcal{H})$ we define the $X_\\varphi$-hypersuface by cutting $X$ with a hyperplane $H_\\varphi$ defined by the linear form $\\langle\\varphi|$ (the $X_\\varphi$-hypersurface of $X$ is $X\\cap H_\\varphi \\subset X$).\n  We prove that when $|\\varphi\\rangle$ ranges over the SLOCC entangl"},"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":"1606.05537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-17T14:41:40Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"21e4e71ddba21b1b901fdb71b8ce3c14e9d1c85dc0537f1c5c2014b32f9d0396","abstract_canon_sha256":"fb7a38283c0fedc4cc1434a05156fc7458b926fdb4509c34640e16590459203c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:27.365434Z","signature_b64":"7Cq2/EMr/L4cWpHZai3Opvb1ypURF1THerfAzyDZjxQSszdYf8Neg3RxT/38ggaI2I9ESByti3uQpGPXTE2VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae1ac5be737508364deea066f484e60f02dd79cc996a9dbb05009e45ac5acd70","last_reissued_at":"2026-05-18T00:57:27.364770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:27.364770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-qutrit entanglement and simple singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"quant-ph","authors_text":"Fr\\'ed\\'eric Holweck, Hamza Jaffali","submitted_at":"2016-06-17T14:41:40Z","abstract_excerpt":"In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. 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