{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SMNS5NPC24HSJYTRP6H2FWS3F5","short_pith_number":"pith:SMNS5NPC","schema_version":"1.0","canonical_sha256":"931b2eb5e2d70f24e2717f8fa2da5b2f7bb45ad0c0c09188dd583135e2e5162c","source":{"kind":"arxiv","id":"1404.3911","version":2},"attestation_state":"computed","paper":{"title":"The secant line variety to the varieties of reducible plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Gimigliano, Anthony V. Geramita, Maria Virginia Catalisano, Yong-Su Shin","submitted_at":"2014-04-15T13:54:37Z","abstract_excerpt":"Let $\\lambda =[d_1,\\dots,d_r]$ be a partition of $d$. Consider the variety $\\mathbb{X}_{2,\\lambda} \\subset \\mathbb{P}^N$, $N={d+2 \\choose 2}-1$, parameterizing forms $F\\in k[x_0,x_1,x_2]_d$ which are the product of $r\\geq 2$ forms $F_1,\\dots,F_r$, with deg$F_i = d_i$. We study the secant line variety $\\sigma_2(\\mathbb{X}_{2,\\lambda})$, and we determine, for all $r$ and $d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many \"unbalanced\" cases."},"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":"1404.3911","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-15T13:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"49803b5a1f0c44eacb6bc6e0e3773c9bd2fe65cac7ecac8f6ac698924d513701","abstract_canon_sha256":"8cdabdc4521d97470a1d633acf6107cd0b71ca24fb694ccbf176cbbe0aa375e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:38.817377Z","signature_b64":"QhYetE5c/tXkfQI8rt0MYlbE8U8QDz0/fhVanybedCEBExCxTraE22zYdJOIi0UzDqfB2eUtiQ70S3JGGQDjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"931b2eb5e2d70f24e2717f8fa2da5b2f7bb45ad0c0c09188dd583135e2e5162c","last_reissued_at":"2026-05-18T02:32:38.816987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:38.816987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The secant line variety to the varieties of reducible plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Gimigliano, Anthony V. Geramita, Maria Virginia Catalisano, Yong-Su Shin","submitted_at":"2014-04-15T13:54:37Z","abstract_excerpt":"Let $\\lambda =[d_1,\\dots,d_r]$ be a partition of $d$. Consider the variety $\\mathbb{X}_{2,\\lambda} \\subset \\mathbb{P}^N$, $N={d+2 \\choose 2}-1$, parameterizing forms $F\\in k[x_0,x_1,x_2]_d$ which are the product of $r\\geq 2$ forms $F_1,\\dots,F_r$, with deg$F_i = d_i$. We study the secant line variety $\\sigma_2(\\mathbb{X}_{2,\\lambda})$, and we determine, for all $r$ and $d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many \"unbalanced\" cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3911","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.3911","created_at":"2026-05-18T02:32:38.817041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3911v2","created_at":"2026-05-18T02:32:38.817041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3911","created_at":"2026-05-18T02:32:38.817041+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMNS5NPC24HS","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMNS5NPC24HSJYTR","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMNS5NPC","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5","json":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5.json","graph_json":"https://pith.science/api/pith-number/SMNS5NPC24HSJYTRP6H2FWS3F5/graph.json","events_json":"https://pith.science/api/pith-number/SMNS5NPC24HSJYTRP6H2FWS3F5/events.json","paper":"https://pith.science/paper/SMNS5NPC"},"agent_actions":{"view_html":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5","download_json":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5.json","view_paper":"https://pith.science/paper/SMNS5NPC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3911&json=true","fetch_graph":"https://pith.science/api/pith-number/SMNS5NPC24HSJYTRP6H2FWS3F5/graph.json","fetch_events":"https://pith.science/api/pith-number/SMNS5NPC24HSJYTRP6H2FWS3F5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5/action/storage_attestation","attest_author":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5/action/author_attestation","sign_citation":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5/action/citation_signature","submit_replication":"https://pith.science/pith/SMNS5NPC24HSJYTRP6H2FWS3F5/action/replication_record"}},"created_at":"2026-05-18T02:32:38.817041+00:00","updated_at":"2026-05-18T02:32:38.817041+00:00"}