{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Z7ADHWX5OP4VJYBW52TVLZ76XC","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":"83a805b006ed96fe8de9828265c75de51d8984fd7ed7febee3d9e733beddd1ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-08-14T19:02:15Z","title_canon_sha256":"5793097cf5f829b21aad828eaf879013f1407ef78d7ba19ba2aead9eb9749edc"},"schema_version":"1.0","source":{"id":"1908.05314","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05314","created_at":"2026-07-05T06:43:42Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05314v4","created_at":"2026-07-05T06:43:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05314","created_at":"2026-07-05T06:43:42Z"},{"alias_kind":"pith_short_12","alias_value":"Z7ADHWX5OP4V","created_at":"2026-07-05T06:43:42Z"},{"alias_kind":"pith_short_16","alias_value":"Z7ADHWX5OP4VJYBW","created_at":"2026-07-05T06:43:42Z"},{"alias_kind":"pith_short_8","alias_value":"Z7ADHWX5","created_at":"2026-07-05T06:43:42Z"}],"graph_snapshots":[{"event_id":"sha256:0ffcb3f138b41a715c470f4bc6384708b8f585283d9795fdcc5c29c08e148b94","target":"graph","created_at":"2026-07-05T06:43:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05314/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents several new results related to the Kakeya problem. First, we establish a geometric inequality which says that collections of direction-separated tubes (thin neighborhoods of line segments that point in different directions) cannot cluster inside thin neighborhoods of low degree algebraic varieties. We use this geometric inequality to obtain a new family of multilinear Kakeya estimates for direction-separated tubes. Using the linear / multilinear theory of Bourgain and Guth, these multilinear Kakeya estimates are converted into Kakeya maximal function estimates. Specifically","authors_text":"Joshua Zahl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-08-14T19:02:15Z","title":"New Kakeya estimates using Gromov's algebraic lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05314","kind":"arxiv","version":4},"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:c05bfa1daa92edff0c45f75f27ba498d3f02ab1feeca1438ce0aca7345d1e9d4","target":"record","created_at":"2026-07-05T06:43:42Z","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":"83a805b006ed96fe8de9828265c75de51d8984fd7ed7febee3d9e733beddd1ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-08-14T19:02:15Z","title_canon_sha256":"5793097cf5f829b21aad828eaf879013f1407ef78d7ba19ba2aead9eb9749edc"},"schema_version":"1.0","source":{"id":"1908.05314","kind":"arxiv","version":4}},"canonical_sha256":"cfc033dafd73f954e036eea755e7feb8bf01ac229d29034a00b5794b2a156ecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfc033dafd73f954e036eea755e7feb8bf01ac229d29034a00b5794b2a156ecd","first_computed_at":"2026-07-05T06:43:42.583181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:42.583181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nms+oa4+9BwHrfK5Bwpnw9BXQeWmtHrV9NAUETVggcf3bH8LsbqhpMLXxcMGWMf6KGVQytEz/kUw2XNV02FyCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:42.583618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05314","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c05bfa1daa92edff0c45f75f27ba498d3f02ab1feeca1438ce0aca7345d1e9d4","sha256:0ffcb3f138b41a715c470f4bc6384708b8f585283d9795fdcc5c29c08e148b94"],"state_sha256":"e40868d2a6192eb2563efeb471543486c5dfc231e633c9e8640ddb51d131b0e6"}