{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3R7V5ZXCHRA7SLXH2HZASSYRSX","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":"d7dab00612e21994044e217a7c37a7830f6e4393ff17aa97433fcc19a0687497","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-07T20:28:08Z","title_canon_sha256":"4085b889ee443da930ee3bbfa6003bae59c06eb6fd41d6bac4f0176896c45f5f"},"schema_version":"1.0","source":{"id":"1109.1573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1573","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1573v2","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1573","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"3R7V5ZXCHRA7","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3R7V5ZXCHRA7SLXH","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3R7V5ZXC","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:bd528ccaca84cf4f76449df46ca5443e8f405f6b789c40b5f7c3d20ee08d79d3","target":"graph","created_at":"2026-05-18T04:12:54Z","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 study the problem of finding the largest possible set of s points and s lines in a projective plane of order q, such that that none of the s points lie on any of the s lines. We prove that s <= 1+(q+1)(\\sqrt{q}-1). We also show that equality can be attained in this bound whenever q is an even power of two.","authors_text":"Douglas R. Stinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-07T20:28:08Z","title":"A Problem Concerning Nonincident Points and Lines in Projective Planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1573","kind":"arxiv","version":2},"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":"sha256:36acb941938079a792b2f39cf0e4cc489c6e62b56c2df2a268472c3c414e8413","target":"record","created_at":"2026-05-18T04:12:54Z","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":"d7dab00612e21994044e217a7c37a7830f6e4393ff17aa97433fcc19a0687497","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-07T20:28:08Z","title_canon_sha256":"4085b889ee443da930ee3bbfa6003bae59c06eb6fd41d6bac4f0176896c45f5f"},"schema_version":"1.0","source":{"id":"1109.1573","kind":"arxiv","version":2}},"canonical_sha256":"dc7f5ee6e23c41f92ee7d1f2094b1195e5110f1493e62623574ded04c9cd9f01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc7f5ee6e23c41f92ee7d1f2094b1195e5110f1493e62623574ded04c9cd9f01","first_computed_at":"2026-05-18T04:12:54.264278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:54.264278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/cjKQDxPV6yv3F5Lzkuk1R1zXnDlCLDzMi3z/MDaLzYj/dAaJDi/1MQvDDieRiC44P9neG88DYCUfcfNDT+nBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:54.264997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36acb941938079a792b2f39cf0e4cc489c6e62b56c2df2a268472c3c414e8413","sha256:bd528ccaca84cf4f76449df46ca5443e8f405f6b789c40b5f7c3d20ee08d79d3"],"state_sha256":"1b21fbf35c6dcc68e3303a36949783edce627c07aafa82dbf2688a613626d321"}