{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FRB2PPQHMBVJOX63SOFLW3GLN3","short_pith_number":"pith:FRB2PPQH","schema_version":"1.0","canonical_sha256":"2c43a7be07606a975fdb938abb6ccb6eef5588c33cfa835b6a14866c8568b4a9","source":{"kind":"arxiv","id":"1605.03530","version":3},"attestation_state":"computed","paper":{"title":"Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Binzhou Xia, Sanming Zhou, Teng Fang, Xin Gui Fang","submitted_at":"2016-05-11T17:41:26Z","abstract_excerpt":"A graph $\\Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $\\Gamma$ with $V(\\Gamma)$ admitting a nontrivial $G$-invariant partition $\\mathcal{B}$ such that there is exactly one edge of $\\Gamma$ between any two distinct blocks of $\\mathcal{B}$. This is achieved by giving a classification of $(G, 2)$-point-transitive and $G$-block-transitive designs $\\mathcal{D}$ together with $G$-orbits $\\Omega$ on the flag set of $\\mathcal{D}$ such that $G_{\\sigma, L"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.03530","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-11T17:41:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4e6c73092a883a21f18ee38808948c2c38379e4ba29093121e608eeef7efa173","abstract_canon_sha256":"2d4b3c62df768b806575452b0e9ece4fde071f46d37daf7bd0ace098fde4018f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:17.899627Z","signature_b64":"DwO3kYBDAKrWrQPwSPLZFE0xMJyz1pDi3n8527mgcUj828EHgFFI5brSYBBXiTn7DVtxAcb9duqzCK62f9uFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c43a7be07606a975fdb938abb6ccb6eef5588c33cfa835b6a14866c8568b4a9","last_reissued_at":"2026-05-18T00:42:17.899032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:17.899032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Binzhou Xia, Sanming Zhou, Teng Fang, Xin Gui Fang","submitted_at":"2016-05-11T17:41:26Z","abstract_excerpt":"A graph $\\Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $\\Gamma$ with $V(\\Gamma)$ admitting a nontrivial $G$-invariant partition $\\mathcal{B}$ such that there is exactly one edge of $\\Gamma$ between any two distinct blocks of $\\mathcal{B}$. This is achieved by giving a classification of $(G, 2)$-point-transitive and $G$-block-transitive designs $\\mathcal{D}$ together with $G$-orbits $\\Omega$ on the flag set of $\\mathcal{D}$ such that $G_{\\sigma, L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03530","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.03530","created_at":"2026-05-18T00:42:17.899113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03530v3","created_at":"2026-05-18T00:42:17.899113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03530","created_at":"2026-05-18T00:42:17.899113+00:00"},{"alias_kind":"pith_short_12","alias_value":"FRB2PPQHMBVJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FRB2PPQHMBVJOX63","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FRB2PPQH","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3","json":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3.json","graph_json":"https://pith.science/api/pith-number/FRB2PPQHMBVJOX63SOFLW3GLN3/graph.json","events_json":"https://pith.science/api/pith-number/FRB2PPQHMBVJOX63SOFLW3GLN3/events.json","paper":"https://pith.science/paper/FRB2PPQH"},"agent_actions":{"view_html":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3","download_json":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3.json","view_paper":"https://pith.science/paper/FRB2PPQH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03530&json=true","fetch_graph":"https://pith.science/api/pith-number/FRB2PPQHMBVJOX63SOFLW3GLN3/graph.json","fetch_events":"https://pith.science/api/pith-number/FRB2PPQHMBVJOX63SOFLW3GLN3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3/action/storage_attestation","attest_author":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3/action/author_attestation","sign_citation":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3/action/citation_signature","submit_replication":"https://pith.science/pith/FRB2PPQHMBVJOX63SOFLW3GLN3/action/replication_record"}},"created_at":"2026-05-18T00:42:17.899113+00:00","updated_at":"2026-05-18T00:42:17.899113+00:00"}