{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NTZMVU77RZLEYG6Z56CBKZVWGS","short_pith_number":"pith:NTZMVU77","schema_version":"1.0","canonical_sha256":"6cf2cad3ff8e564c1bd9ef841566b6348d568af2ee9706a1acb647bba72ceb21","source":{"kind":"arxiv","id":"1304.3322","version":3},"attestation_state":"computed","paper":{"title":"Homogeneous projective varieties with semi-continuous rank function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"A. Petukhov, V. Tsanov","submitted_at":"2013-04-11T14:33:36Z","abstract_excerpt":"Let $\\mathbb X\\subset\\mathbb P(V)$ be a projective variety, which is not contained in a hyperplane. Then every vector $v$ in $V$ can be written as a sum of vectors from the affine cone $X$ over $\\mathbb X$. The minimal number of summands in such a sum is called the rank of $v$. The set of vectors of rank $r$ is denoted by $X_r$ and its projective image by $\\mathbb X_r$. The r-th secant variety of $X$ is defined $\\sigma_r(\\mathbb X):=\\bar{\\sqcup_{s\\le r}\\mathbb X_s}$; it is called tame if $\\sigma_r(\\mathbb X)=\\sqcup_{s\\le r} \\mathbb X_s$ and wild if the closure contains elements of higher rank."},"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":"1304.3322","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-11T14:33:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1ac0772dcd9942ba853e8e144254097a9da756fdb46f360edfd7be21ad0cf915","abstract_canon_sha256":"28b76e3e735180a00b112c7bd264585413f5b80f7f7167a74105bb4a8e42fb84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:36.471687Z","signature_b64":"BE/tD5W2K16DN3CW4sFsopCauqaXGNY6TFdmytOT/b6iD+KFF4wTnLqTNPVsVSHuhmz4OTDGyToATjzLG417AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cf2cad3ff8e564c1bd9ef841566b6348d568af2ee9706a1acb647bba72ceb21","last_reissued_at":"2026-05-18T02:19:36.471116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:36.471116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous projective varieties with semi-continuous rank function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"A. Petukhov, V. Tsanov","submitted_at":"2013-04-11T14:33:36Z","abstract_excerpt":"Let $\\mathbb X\\subset\\mathbb P(V)$ be a projective variety, which is not contained in a hyperplane. Then every vector $v$ in $V$ can be written as a sum of vectors from the affine cone $X$ over $\\mathbb X$. The minimal number of summands in such a sum is called the rank of $v$. The set of vectors of rank $r$ is denoted by $X_r$ and its projective image by $\\mathbb X_r$. The r-th secant variety of $X$ is defined $\\sigma_r(\\mathbb X):=\\bar{\\sqcup_{s\\le r}\\mathbb X_s}$; it is called tame if $\\sigma_r(\\mathbb X)=\\sqcup_{s\\le r} \\mathbb X_s$ and wild if the closure contains elements of higher rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3322","kind":"arxiv","version":3},"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":"1304.3322","created_at":"2026-05-18T02:19:36.471191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.3322v3","created_at":"2026-05-18T02:19:36.471191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3322","created_at":"2026-05-18T02:19:36.471191+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTZMVU77RZLE","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTZMVU77RZLEYG6Z","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTZMVU77","created_at":"2026-05-18T12:27:52.871228+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/NTZMVU77RZLEYG6Z56CBKZVWGS","json":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS.json","graph_json":"https://pith.science/api/pith-number/NTZMVU77RZLEYG6Z56CBKZVWGS/graph.json","events_json":"https://pith.science/api/pith-number/NTZMVU77RZLEYG6Z56CBKZVWGS/events.json","paper":"https://pith.science/paper/NTZMVU77"},"agent_actions":{"view_html":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS","download_json":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS.json","view_paper":"https://pith.science/paper/NTZMVU77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.3322&json=true","fetch_graph":"https://pith.science/api/pith-number/NTZMVU77RZLEYG6Z56CBKZVWGS/graph.json","fetch_events":"https://pith.science/api/pith-number/NTZMVU77RZLEYG6Z56CBKZVWGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS/action/storage_attestation","attest_author":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS/action/author_attestation","sign_citation":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS/action/citation_signature","submit_replication":"https://pith.science/pith/NTZMVU77RZLEYG6Z56CBKZVWGS/action/replication_record"}},"created_at":"2026-05-18T02:19:36.471191+00:00","updated_at":"2026-05-18T02:19:36.471191+00:00"}