{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7X6BUKGDVWF753VZEXVMGHWWHD","short_pith_number":"pith:7X6BUKGD","schema_version":"1.0","canonical_sha256":"fdfc1a28c3ad8bfeeeb925eac31ed638f5429c493392d3e857fbf214ebfeda5c","source":{"kind":"arxiv","id":"1406.5145","version":2},"attestation_state":"computed","paper":{"title":"Geometric lower bounds for generalized ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.AG","authors_text":"Zach Teitler","submitted_at":"2014-06-19T18:45:21Z","abstract_excerpt":"We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of Landsberg and Teitler and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the \"non-Abelian\" catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially symmetric tensors); a special case is the simultaneous Waring decomposition problem for a linear system of polynomials. We generalize the classical Apolarity Lemma to multihomogeneous polyno"},"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":"1406.5145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-19T18:45:21Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"aa7d34922fcab0efa40417fb9e6495323aa68b5f5003498b185f5cc30fd726ee","abstract_canon_sha256":"c884b98bb4e24dd2c5de5c82e1dbaebe58760e8fa8c2d0a264243d4b983eb316"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:09.072510Z","signature_b64":"jRhVLOUaAo3g1NkY+aHVRL0B/LNskIeFt8zU9n7hQ/tQI5mXesoIcGYwH3XjlqgB7Itlq8JUnQ7cx7itYLy1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdfc1a28c3ad8bfeeeb925eac31ed638f5429c493392d3e857fbf214ebfeda5c","last_reissued_at":"2026-05-18T02:48:09.071849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:09.071849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric lower bounds for generalized ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.AG","authors_text":"Zach Teitler","submitted_at":"2014-06-19T18:45:21Z","abstract_excerpt":"We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of Landsberg and Teitler and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the \"non-Abelian\" catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially symmetric tensors); a special case is the simultaneous Waring decomposition problem for a linear system of polynomials. We generalize the classical Apolarity Lemma to multihomogeneous polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5145","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":"1406.5145","created_at":"2026-05-18T02:48:09.071958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5145v2","created_at":"2026-05-18T02:48:09.071958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5145","created_at":"2026-05-18T02:48:09.071958+00:00"},{"alias_kind":"pith_short_12","alias_value":"7X6BUKGDVWF7","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7X6BUKGDVWF753VZ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7X6BUKGD","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08896","citing_title":"A bound for the Waring rank of the determinant via syzygies","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD","json":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD.json","graph_json":"https://pith.science/api/pith-number/7X6BUKGDVWF753VZEXVMGHWWHD/graph.json","events_json":"https://pith.science/api/pith-number/7X6BUKGDVWF753VZEXVMGHWWHD/events.json","paper":"https://pith.science/paper/7X6BUKGD"},"agent_actions":{"view_html":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD","download_json":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD.json","view_paper":"https://pith.science/paper/7X6BUKGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5145&json=true","fetch_graph":"https://pith.science/api/pith-number/7X6BUKGDVWF753VZEXVMGHWWHD/graph.json","fetch_events":"https://pith.science/api/pith-number/7X6BUKGDVWF753VZEXVMGHWWHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD/action/storage_attestation","attest_author":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD/action/author_attestation","sign_citation":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD/action/citation_signature","submit_replication":"https://pith.science/pith/7X6BUKGDVWF753VZEXVMGHWWHD/action/replication_record"}},"created_at":"2026-05-18T02:48:09.071958+00:00","updated_at":"2026-05-18T02:48:09.071958+00:00"}