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Here we classify all P in P^n such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets. For such tensors P, we prove that S(P) has no isolated points."},"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":"1202.3066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-14T15:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"64cde062f070e466a77297551667d8db83122aba92c392691a0c3cfd896a1084","abstract_canon_sha256":"fc6d15f0565b404c60bef7a459f0dc882a13f0f91d8f51fcbcec10583f14dc2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:24.175663Z","signature_b64":"kij8Etnro63VY2eQHK1dbtYo6BRrW/sj89nNQ/pgy8djXEdS0Ebb0I3i7+/kk+YJ+msptcoGKtdHCTbAARQ5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16300527f1f0a9ace7deb9a4f7142a858c7de818c1fb498301d14e69706e4f7b","last_reissued_at":"2026-05-18T04:02:24.175019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:24.175019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sets computing the symmetric tensor rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Luca Chiantini","submitted_at":"2012-02-14T15:38:44Z","abstract_excerpt":"Let n_d denote the degree d Veronese embedding of a projective space P^r. 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