{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6JYV236ZRNDAWMPSOWHV3V46BQ","short_pith_number":"pith:6JYV236Z","schema_version":"1.0","canonical_sha256":"f2715d6fd98b460b31f2758f5dd79e0c3509efa35dc632ff84d2c6b3b348583a","source":{"kind":"arxiv","id":"1209.1664","version":2},"attestation_state":"computed","paper":{"title":"Explicit tensors of border rank at least 2n-1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"J.M. Landsberg","submitted_at":"2012-09-07T22:24:47Z","abstract_excerpt":"For odd n, I write down tensors in C^n\\otimes C^n\\otimes C^n of border rank 2n-1, showing the non-triviality of the Young-flattening equations of Landsberg-Ottaviani. I also study the border rank of the tensors of Alexeev et. al., showing the tensors their tensors T_{2^k}, despite having rank equal to 2^{k+1}-1, have border rank equal to 2^k, the minimum of any concise tensor. I also study the equations of Griesser."},"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":"1209.1664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-09-07T22:24:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b83c9f45c7f571a5b9eb8a50b4bcb00331e9451542bfca2bf2850cf906660933","abstract_canon_sha256":"ac39c58f4420a01102fab598096beba41162b8ddcb2739c9566e6b525db92915"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:38.624275Z","signature_b64":"OEFkFZ7xpDkJgfHPa0ZrgR/4KekGOqCwhLgD0P41vvoeAsDcOjXfnypr8RwCpjCZqXYvcBLgKJzyqoGlJa9zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2715d6fd98b460b31f2758f5dd79e0c3509efa35dc632ff84d2c6b3b348583a","last_reissued_at":"2026-05-18T03:16:38.623822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:38.623822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit tensors of border rank at least 2n-1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"J.M. Landsberg","submitted_at":"2012-09-07T22:24:47Z","abstract_excerpt":"For odd n, I write down tensors in C^n\\otimes C^n\\otimes C^n of border rank 2n-1, showing the non-triviality of the Young-flattening equations of Landsberg-Ottaviani. I also study the border rank of the tensors of Alexeev et. al., showing the tensors their tensors T_{2^k}, despite having rank equal to 2^{k+1}-1, have border rank equal to 2^k, the minimum of any concise tensor. I also study the equations of Griesser."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1664","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":"1209.1664","created_at":"2026-05-18T03:16:38.623894+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.1664v2","created_at":"2026-05-18T03:16:38.623894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1664","created_at":"2026-05-18T03:16:38.623894+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JYV236ZRNDA","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JYV236ZRNDAWMPS","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JYV236Z","created_at":"2026-05-18T12:26:56.085431+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/6JYV236ZRNDAWMPSOWHV3V46BQ","json":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ.json","graph_json":"https://pith.science/api/pith-number/6JYV236ZRNDAWMPSOWHV3V46BQ/graph.json","events_json":"https://pith.science/api/pith-number/6JYV236ZRNDAWMPSOWHV3V46BQ/events.json","paper":"https://pith.science/paper/6JYV236Z"},"agent_actions":{"view_html":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ","download_json":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ.json","view_paper":"https://pith.science/paper/6JYV236Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.1664&json=true","fetch_graph":"https://pith.science/api/pith-number/6JYV236ZRNDAWMPSOWHV3V46BQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6JYV236ZRNDAWMPSOWHV3V46BQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ/action/storage_attestation","attest_author":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ/action/author_attestation","sign_citation":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ/action/citation_signature","submit_replication":"https://pith.science/pith/6JYV236ZRNDAWMPSOWHV3V46BQ/action/replication_record"}},"created_at":"2026-05-18T03:16:38.623894+00:00","updated_at":"2026-05-18T03:16:38.623894+00:00"}