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We prove that the $X$-rank of $q$ is at least $b+1$ for a non-empty codimension $1$ locally closed subset of $\\sigma _b(X)$."},"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":"1706.03633","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:44:58Z","cross_cats_sorted":[],"title_canon_sha256":"5c46a69dbeef38fecacb510a8bb4790ff2cd217a5173bd95127c91323dde8d68","abstract_canon_sha256":"a6c114a50cd9a8180746eee503bf4662abf20717937a3ac8a6bec6047d0fb1ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:12.048509Z","signature_b64":"SGqlTGpEaXmSsYQMBeWGVtSHQNbw6hK5nvIpbRkCrcc+NZWQpFM/QS1K2/+On0XvI4NXTWZi+qzGm3TcuxwtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8d7c7aa0c39ab570ca2196a6a7998167ee2c393783ac005f1d429c42ff0c4c0","last_reissued_at":"2026-05-18T00:39:12.047898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:12.047898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $b$-secant variety of a smooth curve has a codimension $1$ locally closed subset whose points have rank at least $b+1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E. 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