{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XFRT6IBSMBWKUOVACQ32MTIYDA","short_pith_number":"pith:XFRT6IBS","canonical_record":{"source":{"id":"1302.5591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-22T13:50:35Z","cross_cats_sorted":[],"title_canon_sha256":"526024d64462b0374314c84bdf3d8c90c31ae44b6b97709a94d83235a3ed6057","abstract_canon_sha256":"116b357b2b255dbf3e7f552a8dc176e57aab379a2e903c97359295f3c4e7eb95"},"schema_version":"1.0"},"canonical_sha256":"b9633f2032606caa3aa01437a64d18183e8f7199e66d8ab5ee269c64bf83ce0b","source":{"kind":"arxiv","id":"1302.5591","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XFRT6IBSMBWKUOVACQ32MTIYDA","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-22T13:50:35Z","cross_cats_sorted":[],"title_canon_sha256":"526024d64462b0374314c84bdf3d8c90c31ae44b6b97709a94d83235a3ed6057","abstract_canon_sha256":"116b357b2b255dbf3e7f552a8dc176e57aab379a2e903c97359295f3c4e7eb95"},"schema_version":"1.0"},"canonical_sha256":"b9633f2032606caa3aa01437a64d18183e8f7199e66d8ab5ee269c64bf83ce0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:46.322810Z","signature_b64":"DgcEiEZ4d35L4zoSGvvmLVvK57awsQJ779eEvzZ8BuzGJsjXrBtG/MGH6IaxiY+dcBNMlQpe0cN8AMTOW2lWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9633f2032606caa3aa01437a64d18183e8f7199e66d8ab5ee269c64bf83ce0b","last_reissued_at":"2026-05-18T03:32:46.322103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:46.322103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5591","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3nFgRTrejqU8sAA0fHlrXQkju1P5KoIMR/Zf+eNXwA+MTvTxV4jKerRHtrAEJM9r3gnZWeHQHtOrKS+f/2vDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:02.111174Z"},"content_sha256":"de7bc3889736c603d772a460f4715c0be8e9405a7c0304dd510a640ad22f6f4b","schema_version":"1.0","event_id":"sha256:de7bc3889736c603d772a460f4715c0be8e9405a7c0304dd510a640ad22f6f4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XFRT6IBSMBWKUOVACQ32MTIYDA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the size of Kakeya sets in finite vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gohar Kyureghyan, Peter M\\\"uller, Qi Wang","submitted_at":"2013-02-22T13:50:35Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5591","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Li2FJB2Irx2iukLQ8gd2d/klLTAqc25uv83i2ZZRR4oxWbpGWVjgl0eYuIrno6oeB/I2Xb8XQkvQsWW33m9aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:02.111815Z"},"content_sha256":"cf005469be88d13f360f97bd83c87d9e7d6603ed7d60b6a908b2cb2c6cd5480b","schema_version":"1.0","event_id":"sha256:cf005469be88d13f360f97bd83c87d9e7d6603ed7d60b6a908b2cb2c6cd5480b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/bundle.json","state_url":"https://pith.science/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T20:13:02Z","links":{"resolver":"https://pith.science/pith/XFRT6IBSMBWKUOVACQ32MTIYDA","bundle":"https://pith.science/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/bundle.json","state":"https://pith.science/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFRT6IBSMBWKUOVACQ32MTIYDA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZjR3/+reSTml6tvKIfVgbg3WjUork3P6uy7MrmuB3FxhouAo49PVBU27DHTF8U4+lVsAU12UZxGx49UMNZQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:13:02.115619Z","bundle_sha256":"389d4fbbb7feaf2e366173e4a02717fb3b518a546684319155ba72e1a9350cf1"}}