{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6JYV236ZRNDAWMPSOWHV3V46BQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ac39c58f4420a01102fab598096beba41162b8ddcb2739c9566e6b525db92915","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-09-07T22:24:47Z","title_canon_sha256":"b83c9f45c7f571a5b9eb8a50b4bcb00331e9451542bfca2bf2850cf906660933"},"schema_version":"1.0","source":{"id":"1209.1664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1664","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1664v2","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1664","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"6JYV236ZRNDA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6JYV236ZRNDAWMPS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6JYV236Z","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7e5edb710dbd63bd774e0a2e2593c96703a79da1df06423916a84a736e49159c","target":"graph","created_at":"2026-05-18T03:16:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"J.M. Landsberg","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-09-07T22:24:47Z","title":"Explicit tensors of border rank at least 2n-1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1664","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9c33c6e054a45aab61c6a8b4b09dd17b9400c4a7f89be74599751fdcd2c2f744","target":"record","created_at":"2026-05-18T03:16:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac39c58f4420a01102fab598096beba41162b8ddcb2739c9566e6b525db92915","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-09-07T22:24:47Z","title_canon_sha256":"b83c9f45c7f571a5b9eb8a50b4bcb00331e9451542bfca2bf2850cf906660933"},"schema_version":"1.0","source":{"id":"1209.1664","kind":"arxiv","version":2}},"canonical_sha256":"f2715d6fd98b460b31f2758f5dd79e0c3509efa35dc632ff84d2c6b3b348583a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2715d6fd98b460b31f2758f5dd79e0c3509efa35dc632ff84d2c6b3b348583a","first_computed_at":"2026-05-18T03:16:38.623822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:38.623822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OEFkFZ7xpDkJgfHPa0ZrgR/4KekGOqCwhLgD0P41vvoeAsDcOjXfnypr8RwCpjCZqXYvcBLgKJzyqoGlJa9zCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:38.624275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c33c6e054a45aab61c6a8b4b09dd17b9400c4a7f89be74599751fdcd2c2f744","sha256:7e5edb710dbd63bd774e0a2e2593c96703a79da1df06423916a84a736e49159c"],"state_sha256":"eedfbc7849d8880735f712c0babf35a18f425d0bb8c8fd1670fd544b74500f5a"}