{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UJB3J6WM4KQNJ2LJTL7YJGZ7UH","short_pith_number":"pith:UJB3J6WM","canonical_record":{"source":{"id":"1201.4912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-24T04:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"007f1678632c343545e46b7ff72c1a3205a8c1425a9149c597b288c06b0a122d","abstract_canon_sha256":"227da068eec3b1dca1c0d2c87a4dd9fee5df711c87e713c96f32ff25cd3529de"},"schema_version":"1.0"},"canonical_sha256":"a243b4facce2a0d4e9699aff849b3fa1eabfa45c8f4874d1a2940cbf04400b81","source":{"kind":"arxiv","id":"1201.4912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4912","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4912v1","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4912","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"UJB3J6WM4KQN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UJB3J6WM4KQNJ2LJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UJB3J6WM","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UJB3J6WM4KQNJ2LJTL7YJGZ7UH","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-24T04:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"007f1678632c343545e46b7ff72c1a3205a8c1425a9149c597b288c06b0a122d","abstract_canon_sha256":"227da068eec3b1dca1c0d2c87a4dd9fee5df711c87e713c96f32ff25cd3529de"},"schema_version":"1.0"},"canonical_sha256":"a243b4facce2a0d4e9699aff849b3fa1eabfa45c8f4874d1a2940cbf04400b81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:04.819560Z","signature_b64":"H+iVjWu7NEfCV2V/UIy+y5T8FtD+YasjXsmpBBfSF8QzCW14syFegUlk68es69BEOBH2kvsoq2cWAUknNRBWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a243b4facce2a0d4e9699aff849b3fa1eabfa45c8f4874d1a2940cbf04400b81","last_reissued_at":"2026-05-18T04:04:04.819128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:04.819128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4912","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":"2026-05-18T04:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuZHrL7YId/Un3W86QNz+tLoq/Za697Z7+fncY78ShwUkKsBeYs9LcAzcdUeFiBn7f2GkcQvfaFq9hnG4/fTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:45:20.111980Z"},"content_sha256":"c5704b4c1ddd8f92462ad295d595c8baa1a37d080d0ab30634c834072cec64d0","schema_version":"1.0","event_id":"sha256:c5704b4c1ddd8f92462ad295d595c8baa1a37d080d0ab30634c834072cec64d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UJB3J6WM4KQNJ2LJTL7YJGZ7UH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal Graphs Without 4-Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Evan D. Nash, Frank A. Firke, Jason Williford, Peter M. Kosek","submitted_at":"2012-01-24T04:10:51Z","abstract_excerpt":"We prove an upper bound for the number of edges a C4-free graph on q^2 + q vertices can contain for q even. This upper bound is achieved whenever there is an orthogonal polarity graph of a plane of even order q."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4912","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":"2026-05-18T04:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQb0QzQX5jrGOUuCJhfAUFaolygu0jWHwX9K9StRpMjDjghxhYxFUOFu8TlbCryOI1qsP3OIMbDM7+s8cVORBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:45:20.112400Z"},"content_sha256":"3bec65656b85065f25f22e3a524961b69d490f60226cbb2a1eb37bb41e4bf989","schema_version":"1.0","event_id":"sha256:3bec65656b85065f25f22e3a524961b69d490f60226cbb2a1eb37bb41e4bf989"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/bundle.json","state_url":"https://pith.science/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/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":"2026-05-27T12:45:20Z","links":{"resolver":"https://pith.science/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH","bundle":"https://pith.science/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/bundle.json","state":"https://pith.science/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJB3J6WM4KQNJ2LJTL7YJGZ7UH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UJB3J6WM4KQNJ2LJTL7YJGZ7UH","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":"227da068eec3b1dca1c0d2c87a4dd9fee5df711c87e713c96f32ff25cd3529de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-24T04:10:51Z","title_canon_sha256":"007f1678632c343545e46b7ff72c1a3205a8c1425a9149c597b288c06b0a122d"},"schema_version":"1.0","source":{"id":"1201.4912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4912","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4912v1","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4912","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"UJB3J6WM4KQN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UJB3J6WM4KQNJ2LJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UJB3J6WM","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:3bec65656b85065f25f22e3a524961b69d490f60226cbb2a1eb37bb41e4bf989","target":"graph","created_at":"2026-05-18T04:04:04Z","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":"We prove an upper bound for the number of edges a C4-free graph on q^2 + q vertices can contain for q even. This upper bound is achieved whenever there is an orthogonal polarity graph of a plane of even order q.","authors_text":"Evan D. Nash, Frank A. Firke, Jason Williford, Peter M. Kosek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-24T04:10:51Z","title":"Extremal Graphs Without 4-Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4912","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:c5704b4c1ddd8f92462ad295d595c8baa1a37d080d0ab30634c834072cec64d0","target":"record","created_at":"2026-05-18T04:04:04Z","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":"227da068eec3b1dca1c0d2c87a4dd9fee5df711c87e713c96f32ff25cd3529de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-24T04:10:51Z","title_canon_sha256":"007f1678632c343545e46b7ff72c1a3205a8c1425a9149c597b288c06b0a122d"},"schema_version":"1.0","source":{"id":"1201.4912","kind":"arxiv","version":1}},"canonical_sha256":"a243b4facce2a0d4e9699aff849b3fa1eabfa45c8f4874d1a2940cbf04400b81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a243b4facce2a0d4e9699aff849b3fa1eabfa45c8f4874d1a2940cbf04400b81","first_computed_at":"2026-05-18T04:04:04.819128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:04.819128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H+iVjWu7NEfCV2V/UIy+y5T8FtD+YasjXsmpBBfSF8QzCW14syFegUlk68es69BEOBH2kvsoq2cWAUknNRBWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:04.819560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5704b4c1ddd8f92462ad295d595c8baa1a37d080d0ab30634c834072cec64d0","sha256:3bec65656b85065f25f22e3a524961b69d490f60226cbb2a1eb37bb41e4bf989"],"state_sha256":"908609ac39ba46ce7f39e1438514b1e36c2b5a5f02a2856931d999fdf7d1e591"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPUzHAgyOAHGolzlzclMevuF8EGWJ9tt6PgSbipEi79EIIkM0YwazNZCKKp6rb5JJTPwItr3OA3DJuPJtaSCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:45:20.114936Z","bundle_sha256":"d27fd9ff461b12c0e1828d3f02a55be807ad7b77bf75a7e770885070e99fa046"}}