{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GVQC5F7YKYJP76KKM2HRYLMCBZ","short_pith_number":"pith:GVQC5F7Y","canonical_record":{"source":{"id":"1303.0473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"ad0f44eb666bfb9697531c3a2c502bf86a71934745e1521576b31d78d3a3319a","abstract_canon_sha256":"46aa7f713d748645998e9d9a1efe590a4a573e9438d6efb429af434fc1d773fe"},"schema_version":"1.0"},"canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","source":{"kind":"arxiv","id":"1303.0473","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0473","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0473v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0473","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"GVQC5F7YKYJP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GVQC5F7YKYJP76KK","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GVQC5F7Y","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GVQC5F7YKYJP76KKM2HRYLMCBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"ad0f44eb666bfb9697531c3a2c502bf86a71934745e1521576b31d78d3a3319a","abstract_canon_sha256":"46aa7f713d748645998e9d9a1efe590a4a573e9438d6efb429af434fc1d773fe"},"schema_version":"1.0"},"canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:55.904648Z","signature_b64":"J+eVTtN9FHZjng/tOdPdkfqj97rI9ic+24wOrHAaauJc03/nhtmQ4F+2fQ+vYDOXcDsBr4EVLyHOaWw8ioTPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","last_reissued_at":"2026-05-18T03:31:55.903966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:55.903966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0473","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPCFkkX0Kg4KoJ/MhHi7o+4+/aNFofN09uQecCnEAqvCQfMZPi8H63N7f0zyB5UhMx/0MFOL5A3UuK/eCyBACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:00.438751Z"},"content_sha256":"569cc1128925ddcb7d80702e115dec33fac0c6364f8624c5e5b99a65070290a1","schema_version":"1.0","event_id":"sha256:569cc1128925ddcb7d80702e115dec33fac0c6364f8624c5e5b99a65070290a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GVQC5F7YKYJP76KKM2HRYLMCBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a family of diamond-free strongly regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie","submitted_at":"2013-03-03T07:57:58Z","abstract_excerpt":"The existence of a partial quadrangle ${\\mathsf{PQ}}(s, t, \\mu)$ is equivalent to the existence of a diamond-free strongly regular graph ${\\mathsf{SRG}}(1+s(t+1)+s^2t(t+1)/\\mu, s(t+1), s-1, \\mu)$. Recently, it is shown that there exists a ${\\mathsf{PQ}}(2, (n^3+3n^2-2)/2, n^2+n)$ if and only if $n\\in\\{1, 2, 4\\}$. Let $\\mathcal{S}$ be a ${\\mathsf{PQ}}(3,(n+3)(n^2-1)/3, n^2+n)$ such that for every two non-collinear points $p_1$ and $p_2$, there is a point $q$ non-collinear with $p_1$, $p_2$, and all points collinear with both $p_1$ and $p_2$. In this article, we establish that $\\mathcal{S}$ exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0473","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6dByDH245uMfnCrfm2ZwCX8jem/wRBvuOpBY3tAV4s6S0ZRiWjLD3kHJcxoJCWuz7oT6p3ORdMWNKwhD6lCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:00.439129Z"},"content_sha256":"f41b0ddf26a82245a623e8a4bb9e5b3e2096ad87f7601c8d377fa52c3dbfcb2c","schema_version":"1.0","event_id":"sha256:f41b0ddf26a82245a623e8a4bb9e5b3e2096ad87f7601c8d377fa52c3dbfcb2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/bundle.json","state_url":"https://pith.science/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/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":"2026-06-23T07:30:00Z","links":{"resolver":"https://pith.science/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ","bundle":"https://pith.science/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/bundle.json","state":"https://pith.science/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GVQC5F7YKYJP76KKM2HRYLMCBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GVQC5F7YKYJP76KKM2HRYLMCBZ","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":"46aa7f713d748645998e9d9a1efe590a4a573e9438d6efb429af434fc1d773fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","title_canon_sha256":"ad0f44eb666bfb9697531c3a2c502bf86a71934745e1521576b31d78d3a3319a"},"schema_version":"1.0","source":{"id":"1303.0473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0473","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0473v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0473","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"GVQC5F7YKYJP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GVQC5F7YKYJP76KK","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GVQC5F7Y","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:f41b0ddf26a82245a623e8a4bb9e5b3e2096ad87f7601c8d377fa52c3dbfcb2c","target":"graph","created_at":"2026-05-18T03:31:55Z","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":"The existence of a partial quadrangle ${\\mathsf{PQ}}(s, t, \\mu)$ is equivalent to the existence of a diamond-free strongly regular graph ${\\mathsf{SRG}}(1+s(t+1)+s^2t(t+1)/\\mu, s(t+1), s-1, \\mu)$. Recently, it is shown that there exists a ${\\mathsf{PQ}}(2, (n^3+3n^2-2)/2, n^2+n)$ if and only if $n\\in\\{1, 2, 4\\}$. Let $\\mathcal{S}$ be a ${\\mathsf{PQ}}(3,(n+3)(n^2-1)/3, n^2+n)$ such that for every two non-collinear points $p_1$ and $p_2$, there is a point $q$ non-collinear with $p_1$, $p_2$, and all points collinear with both $p_1$ and $p_2$. In this article, we establish that $\\mathcal{S}$ exis","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","title":"On a family of diamond-free strongly regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0473","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":"sha256:569cc1128925ddcb7d80702e115dec33fac0c6364f8624c5e5b99a65070290a1","target":"record","created_at":"2026-05-18T03:31:55Z","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":"46aa7f713d748645998e9d9a1efe590a4a573e9438d6efb429af434fc1d773fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","title_canon_sha256":"ad0f44eb666bfb9697531c3a2c502bf86a71934745e1521576b31d78d3a3319a"},"schema_version":"1.0","source":{"id":"1303.0473","kind":"arxiv","version":1}},"canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","first_computed_at":"2026-05-18T03:31:55.903966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:55.903966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+eVTtN9FHZjng/tOdPdkfqj97rI9ic+24wOrHAaauJc03/nhtmQ4F+2fQ+vYDOXcDsBr4EVLyHOaWw8ioTPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:55.904648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569cc1128925ddcb7d80702e115dec33fac0c6364f8624c5e5b99a65070290a1","sha256:f41b0ddf26a82245a623e8a4bb9e5b3e2096ad87f7601c8d377fa52c3dbfcb2c"],"state_sha256":"05cc776f1ac607259531279f5dfc03a2404da3ccd13fa90c0a28956d44e2e80d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bipOCz0evvZenGv2So7Pe+yrSTHuey1+SC5Tw3BjCQk3tgxDE6df8rG//eiXoEY2cqxYxUQqVXoEG9091p1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:30:00.441272Z","bundle_sha256":"71613d30261a0322ff9c8e87a0896f0944155980b2c5b94d0e8403207269ee27"}}