{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:US2O364HEMSWVZ5SSDKG66VK44","short_pith_number":"pith:US2O364H","schema_version":"1.0","canonical_sha256":"a4b4edfb8723256ae7b290d46f7aaae7232e85bad47597550608c9e6525c6fa6","source":{"kind":"arxiv","id":"1904.04299","version":1},"attestation_state":"computed","paper":{"title":"More barriers for rank methods, via a \"numeric to symbolic\" transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"Ankit Garg, Avi Wigderson, Rafael Oliveira, Visu Makam","submitted_at":"2019-04-08T19:06:45Z","abstract_excerpt":"We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural lifting (aka escalation) techniques. For example, we prove that even optimal rank lower bounds on $k$-tensors cannot yield non-trivial lower bounds on the rank of $d$-tensors, for any constant $d>k$. This significantly extends recent barrier results on the limits of (matrix) rank methods by Efremenko, Garg, Oliveira and Wigderson, which handles the (very important) case $k=2$.\n  Our generalization requires the development of new technical tools and results in algebraic geometry, which are intere"},"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":"1904.04299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-04-08T19:06:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"544896632232c8941bcb6ac14d65c49be4a53f4f6a7ce704033bc2a031f6a180","abstract_canon_sha256":"a78d49fbc9fac5fb47486d7d6ef5957a2b49bafb571abb3c92624e712b3a5f72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:59.354805Z","signature_b64":"3ZHOnSFvE7FpQySkWl+YUWL6CoAHlnFkB8kKyxj8y1AmFL2AfUCFZ8Wd/WHjeGsJfux5XFo++baIbyBKU7CDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4b4edfb8723256ae7b290d46f7aaae7232e85bad47597550608c9e6525c6fa6","last_reissued_at":"2026-05-17T23:48:59.354443Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:59.354443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More barriers for rank methods, via a \"numeric to symbolic\" transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"Ankit Garg, Avi Wigderson, Rafael Oliveira, Visu Makam","submitted_at":"2019-04-08T19:06:45Z","abstract_excerpt":"We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural lifting (aka escalation) techniques. For example, we prove that even optimal rank lower bounds on $k$-tensors cannot yield non-trivial lower bounds on the rank of $d$-tensors, for any constant $d>k$. This significantly extends recent barrier results on the limits of (matrix) rank methods by Efremenko, Garg, Oliveira and Wigderson, which handles the (very important) case $k=2$.\n  Our generalization requires the development of new technical tools and results in algebraic geometry, which are intere"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04299","kind":"arxiv","version":1},"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":"1904.04299","created_at":"2026-05-17T23:48:59.354503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.04299v1","created_at":"2026-05-17T23:48:59.354503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04299","created_at":"2026-05-17T23:48:59.354503+00:00"},{"alias_kind":"pith_short_12","alias_value":"US2O364HEMSW","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"US2O364HEMSWVZ5S","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"US2O364H","created_at":"2026-05-18T12:33:30.264802+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/US2O364HEMSWVZ5SSDKG66VK44","json":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44.json","graph_json":"https://pith.science/api/pith-number/US2O364HEMSWVZ5SSDKG66VK44/graph.json","events_json":"https://pith.science/api/pith-number/US2O364HEMSWVZ5SSDKG66VK44/events.json","paper":"https://pith.science/paper/US2O364H"},"agent_actions":{"view_html":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44","download_json":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44.json","view_paper":"https://pith.science/paper/US2O364H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.04299&json=true","fetch_graph":"https://pith.science/api/pith-number/US2O364HEMSWVZ5SSDKG66VK44/graph.json","fetch_events":"https://pith.science/api/pith-number/US2O364HEMSWVZ5SSDKG66VK44/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44/action/timestamp_anchor","attest_storage":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44/action/storage_attestation","attest_author":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44/action/author_attestation","sign_citation":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44/action/citation_signature","submit_replication":"https://pith.science/pith/US2O364HEMSWVZ5SSDKG66VK44/action/replication_record"}},"created_at":"2026-05-17T23:48:59.354503+00:00","updated_at":"2026-05-17T23:48:59.354503+00:00"}