{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T5EJG2MY3D76AT3GJD2KW5RWOI","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":"c392214623851b76ceb0e1d34154d09ca6a24e511da4297b2199182ef3eec5db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T23:56:57Z","title_canon_sha256":"28b33d1f81c383bc8cba558f3850c670a12a1883e315b39e861d8565db85c414"},"schema_version":"1.0","source":{"id":"1611.00084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00084","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00084v1","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00084","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"pith_short_12","alias_value":"T5EJG2MY3D76","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T5EJG2MY3D76AT3G","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T5EJG2MY","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:4d70ea85c68449fc80d8f54a7a9a6a82d9db55b0634ccbbbb2bc28f05261afa8","target":"graph","created_at":"2026-05-18T01:00:41Z","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"},"paper":{"abstract_excerpt":"In this paper, we prove that the largest pure partial plane of order 6 has size 25. At the same time, we classify all pure partial planes of order 6 and size 25 up to isomorphism. Our major approach is computer search. The search space is very large so we use combinatorial arguments to rule out some of the cases. For the remaining cases, we subdivide each search by phases and use multiple checks to reduce search space via symmetry.","authors_text":"Yibo Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T23:56:57Z","title":"The Largest Pure Partial Planes of Order 6 Have Size 25"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00084","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:e4c7948802e67e28d58121fe659d76219380d5f65984327a1e8f69f151f4c93e","target":"record","created_at":"2026-05-18T01:00:41Z","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":"c392214623851b76ceb0e1d34154d09ca6a24e511da4297b2199182ef3eec5db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T23:56:57Z","title_canon_sha256":"28b33d1f81c383bc8cba558f3850c670a12a1883e315b39e861d8565db85c414"},"schema_version":"1.0","source":{"id":"1611.00084","kind":"arxiv","version":1}},"canonical_sha256":"9f48936998d8ffe04f6648f4ab7636721b69767d757df3302f29316eb022e098","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f48936998d8ffe04f6648f4ab7636721b69767d757df3302f29316eb022e098","first_computed_at":"2026-05-18T01:00:41.464672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:41.464672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4Q0RxWyYJr/hbn2wDz1R85xC8ZBm3nnbPlDT/4XkoBu8Lot/7Fjzhfc29QMsgOAwCc1YUf1Y06oQedt91AkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:41.465179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4c7948802e67e28d58121fe659d76219380d5f65984327a1e8f69f151f4c93e","sha256:4d70ea85c68449fc80d8f54a7a9a6a82d9db55b0634ccbbbb2bc28f05261afa8"],"state_sha256":"ca4b18f02d7b608de83660fe5cefd0e290bae633b8ae1df303ddd4d3bfbf4952"}