{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:CQWMD4MVX5YQCUKEUBQLHE2AMA","short_pith_number":"pith:CQWMD4MV","schema_version":"1.0","canonical_sha256":"142cc1f195bf71015144a060b393406018e734f39773320c66e0a3032f5f3be9","source":{"kind":"arxiv","id":"0909.4262","version":5},"attestation_state":"computed","paper":{"title":"Ranks of tensors and a generalization of secant varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaros{\\l}aw Buczy\\'nski, J. M. Landsberg","submitted_at":"2009-09-23T18:09:26Z","abstract_excerpt":"We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \\otimes C^b \\otimes C^b. We review the literature from a geometric perspective."},"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":"0909.4262","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-23T18:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"d2985cd34216f762160f2bab65590b0d07e676d2bebd4b512ded8e01ba7862a8","abstract_canon_sha256":"b1c6a90ff42d6c9fcdf581985eba7933413ff5840c6f7736183d56793802d21a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:50.727939Z","signature_b64":"OUhLDjaXQympMZz31ZWatnhddZvZjeY6ozwCjm/tMuJugMfgmycV9HZYQF/EJIFQ27eLe8G8H75d2Ug1c8n8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"142cc1f195bf71015144a060b393406018e734f39773320c66e0a3032f5f3be9","last_reissued_at":"2026-05-18T02:50:50.727423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:50.727423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ranks of tensors and a generalization of secant varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaros{\\l}aw Buczy\\'nski, J. M. Landsberg","submitted_at":"2009-09-23T18:09:26Z","abstract_excerpt":"We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \\otimes C^b \\otimes C^b. We review the literature from a geometric perspective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4262","kind":"arxiv","version":5},"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":"0909.4262","created_at":"2026-05-18T02:50:50.727495+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.4262v5","created_at":"2026-05-18T02:50:50.727495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4262","created_at":"2026-05-18T02:50:50.727495+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQWMD4MVX5YQ","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQWMD4MVX5YQCUKE","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQWMD4MV","created_at":"2026-05-18T12:25:59.703012+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/CQWMD4MVX5YQCUKEUBQLHE2AMA","json":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA.json","graph_json":"https://pith.science/api/pith-number/CQWMD4MVX5YQCUKEUBQLHE2AMA/graph.json","events_json":"https://pith.science/api/pith-number/CQWMD4MVX5YQCUKEUBQLHE2AMA/events.json","paper":"https://pith.science/paper/CQWMD4MV"},"agent_actions":{"view_html":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA","download_json":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA.json","view_paper":"https://pith.science/paper/CQWMD4MV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.4262&json=true","fetch_graph":"https://pith.science/api/pith-number/CQWMD4MVX5YQCUKEUBQLHE2AMA/graph.json","fetch_events":"https://pith.science/api/pith-number/CQWMD4MVX5YQCUKEUBQLHE2AMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA/action/storage_attestation","attest_author":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA/action/author_attestation","sign_citation":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA/action/citation_signature","submit_replication":"https://pith.science/pith/CQWMD4MVX5YQCUKEUBQLHE2AMA/action/replication_record"}},"created_at":"2026-05-18T02:50:50.727495+00:00","updated_at":"2026-05-18T02:50:50.727495+00:00"}