{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2ROK2WO2FHWV5GYVANH7Y6R5SW","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":"9bb1c2b3dd1ad80638c951048e1a9111cfd4d8e2cda9f4da18507516189c7087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T09:24:19Z","title_canon_sha256":"d75c5ada516b40dcee6bce800d1acf00efda853651a0350a99f9e7c8349b8b31"},"schema_version":"1.0","source":{"id":"1609.04962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04962","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04962v3","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04962","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"2ROK2WO2FHWV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2ROK2WO2FHWV5GYV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2ROK2WO2","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:ceb9a1893ddf68db3dd9c4b895294eaab8c7e09985752c98c6f7bf51c01fb1bf","target":"graph","created_at":"2026-05-18T00:04:37Z","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":"A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we focus on commutative quasi-thin weakly distance-regular digraphs, and classify such digraphs with valency more than 3. As a result, this family of digraphs are completely determined.","authors_text":"Benjian Lv, Kaishun Wang, Yuefeng Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T09:24:19Z","title":"Quasi-thin weakly distance-regular digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04962","kind":"arxiv","version":3},"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":"sha256:1a9cff2002a5c71da7d180812d303f4e2bcfa3f7e21e6795fef4e8c6062a864f","target":"record","created_at":"2026-05-18T00:04:37Z","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":"9bb1c2b3dd1ad80638c951048e1a9111cfd4d8e2cda9f4da18507516189c7087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T09:24:19Z","title_canon_sha256":"d75c5ada516b40dcee6bce800d1acf00efda853651a0350a99f9e7c8349b8b31"},"schema_version":"1.0","source":{"id":"1609.04962","kind":"arxiv","version":3}},"canonical_sha256":"d45cad59da29ed5e9b15034ffc7a3d95bf9a0973bd7033cace84b7202bd1da49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d45cad59da29ed5e9b15034ffc7a3d95bf9a0973bd7033cace84b7202bd1da49","first_computed_at":"2026-05-18T00:04:37.709275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:37.709275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khBL+o7h2uYgzI5QMCCrVWOBC0jsOcBNRxd6aiwYCPegRF+XHw6XJjMcsZb5mQ/IGObQ0s0XTo3aCZNllQkjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:37.709720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a9cff2002a5c71da7d180812d303f4e2bcfa3f7e21e6795fef4e8c6062a864f","sha256:ceb9a1893ddf68db3dd9c4b895294eaab8c7e09985752c98c6f7bf51c01fb1bf"],"state_sha256":"c469ff680e08f1283165bc53e9cb59792e74795cefbf46063195f94d9ba3ea02"}