{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MEYXHPM3NPWNGYAXDALQGZGFZ4","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":"fbcc45c4008e50e888e113d333d0c198d442b02dec54db5fd9bd400a120a4ed2","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-24T21:08:02Z","title_canon_sha256":"f39b8b718ea8722eee543afd33c36a5c575b0339a231a8fd2622199055770c02"},"schema_version":"1.0","source":{"id":"2502.17655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.17655","created_at":"2026-07-05T10:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"2502.17655v1","created_at":"2026-07-05T10:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.17655","created_at":"2026-07-05T10:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"MEYXHPM3NPWN","created_at":"2026-07-05T10:19:41Z"},{"alias_kind":"pith_short_16","alias_value":"MEYXHPM3NPWNGYAX","created_at":"2026-07-05T10:19:41Z"},{"alias_kind":"pith_short_8","alias_value":"MEYXHPM3","created_at":"2026-07-05T10:19:41Z"}],"graph_snapshots":[{"event_id":"sha256:b9800bbe3d7f019b0393ab592516ec15aa3a35dae3828cceecde60c6e1189001","target":"graph","created_at":"2026-07-05T10:19:41Z","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/2502.17655/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study sets of $\\delta$ tubes in $\\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almost maximal volume. As a consequence, we prove that every Kakeya set in $\\mathbb{R}^3$ has Minkowski and Hausdorff dimension 3.","authors_text":"Hong Wang, Joshua Zahl","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-24T21:08:02Z","title":"Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17655","kind":"arxiv","version":1},"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":"sha256:30ff91a983ef3c3b9798b77436f1a12a694f2dd47ddad2ecc3e7e9297f119573","target":"record","created_at":"2026-07-05T10:19:41Z","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":"fbcc45c4008e50e888e113d333d0c198d442b02dec54db5fd9bd400a120a4ed2","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-24T21:08:02Z","title_canon_sha256":"f39b8b718ea8722eee543afd33c36a5c575b0339a231a8fd2622199055770c02"},"schema_version":"1.0","source":{"id":"2502.17655","kind":"arxiv","version":1}},"canonical_sha256":"613173bd9b6becd3601718170364c5cf3415fe0b99f43eb5685dd199b8b97399","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"613173bd9b6becd3601718170364c5cf3415fe0b99f43eb5685dd199b8b97399","first_computed_at":"2026-07-05T10:19:41.969914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:19:41.969914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hy+QPyCsWTEA/mLkNf4YjU0YllIfxl14/xnsRX6P3zoZrPlY8zf1E3FeXLsFEX7LdrDHrwZl+edepr/QZPObDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:19:41.970341Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.17655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30ff91a983ef3c3b9798b77436f1a12a694f2dd47ddad2ecc3e7e9297f119573","sha256:b9800bbe3d7f019b0393ab592516ec15aa3a35dae3828cceecde60c6e1189001"],"state_sha256":"b5b1a72aa0f86f99a77e78228ba5910e968ada5c42897bbf95cb9e20991efd0d"}