{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XFRT6IBSMBWKUOVACQ32MTIYDA","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":"116b357b2b255dbf3e7f552a8dc176e57aab379a2e903c97359295f3c4e7eb95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-22T13:50:35Z","title_canon_sha256":"526024d64462b0374314c84bdf3d8c90c31ae44b6b97709a94d83235a3ed6057"},"schema_version":"1.0","source":{"id":"1302.5591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5591","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5591v1","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5591","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"XFRT6IBSMBWK","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XFRT6IBSMBWKUOVA","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XFRT6IBS","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:cf005469be88d13f360f97bd83c87d9e7d6603ed7d60b6a908b2cb2c6cd5480b","target":"graph","created_at":"2026-05-18T03:32:46Z","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 a finite field GF(q) a Kakeya set K is a subset of GF(q)^n that contains a line in every direction. This paper derives new upper bounds on the minimum size of Kakeya sets when q is even.","authors_text":"Gohar Kyureghyan, Peter M\\\"uller, Qi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-22T13:50:35Z","title":"On the size of Kakeya sets in finite vector spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5591","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:de7bc3889736c603d772a460f4715c0be8e9405a7c0304dd510a640ad22f6f4b","target":"record","created_at":"2026-05-18T03:32:46Z","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":"116b357b2b255dbf3e7f552a8dc176e57aab379a2e903c97359295f3c4e7eb95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-22T13:50:35Z","title_canon_sha256":"526024d64462b0374314c84bdf3d8c90c31ae44b6b97709a94d83235a3ed6057"},"schema_version":"1.0","source":{"id":"1302.5591","kind":"arxiv","version":1}},"canonical_sha256":"b9633f2032606caa3aa01437a64d18183e8f7199e66d8ab5ee269c64bf83ce0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9633f2032606caa3aa01437a64d18183e8f7199e66d8ab5ee269c64bf83ce0b","first_computed_at":"2026-05-18T03:32:46.322103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:46.322103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DgcEiEZ4d35L4zoSGvvmLVvK57awsQJ779eEvzZ8BuzGJsjXrBtG/MGH6IaxiY+dcBNMlQpe0cN8AMTOW2lWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:46.322810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de7bc3889736c603d772a460f4715c0be8e9405a7c0304dd510a640ad22f6f4b","sha256:cf005469be88d13f360f97bd83c87d9e7d6603ed7d60b6a908b2cb2c6cd5480b"],"state_sha256":"3d97beaca3396d0ff12ede24030fe16239e65fb6ff476086f291b48c105c3400"}