{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VPUWGJ3NO6A72CC7OAX4DNX7ZT","short_pith_number":"pith:VPUWGJ3N","schema_version":"1.0","canonical_sha256":"abe963276d7781fd085f702fc1b6ffcce141154228e980cec5af3aaed028b464","source":{"kind":"arxiv","id":"1908.04551","version":1},"attestation_state":"computed","paper":{"title":"Existence of non-Cayley Haar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Istv\\'an Kov\\'acs, Jie Wang, Yan-Quan Feng","submitted_at":"2019-08-13T09:06:16Z","abstract_excerpt":"A Cayley graph of a group $H$ is a finite simple graph $\\Gamma$ such that its automorphism group ${\\rm Aut}(\\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\\Sigma$ such that ${\\rm Aut}(\\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\\Sigma)$ and the $H$-orbits are equal to the partite sets of $\\Sigma$. It is well-known that every Haar graph of finite abelian groups is a Cayley graph. In this paper, we prove that every finite non-abelian group admits a non-Cayley Haar graph ex"},"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":"1908.04551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-13T09:06:16Z","cross_cats_sorted":[],"title_canon_sha256":"a3934f1f80f877b8c71ade6fd6d056cecf7ee6888de1e84b0fce0efec372df4e","abstract_canon_sha256":"a8dcc835a8419c8e390bd0b6937b6835cc125857326c8fc007787e36c4334ac7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:55:14.694592Z","signature_b64":"5GPNl6+TZl99sk4k88fIBL1Y2pRIXJ2ngGsmXuXl9iWyXvO9tj1cXouLaBfLHFa7PZuEv+1PDu6ESHBeGw81BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe963276d7781fd085f702fc1b6ffcce141154228e980cec5af3aaed028b464","last_reissued_at":"2026-07-04T23:55:14.694223Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:55:14.694223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of non-Cayley Haar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Istv\\'an Kov\\'acs, Jie Wang, Yan-Quan Feng","submitted_at":"2019-08-13T09:06:16Z","abstract_excerpt":"A Cayley graph of a group $H$ is a finite simple graph $\\Gamma$ such that its automorphism group ${\\rm Aut}(\\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\\Sigma$ such that ${\\rm Aut}(\\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\\Sigma)$ and the $H$-orbits are equal to the partite sets of $\\Sigma$. It is well-known that every Haar graph of finite abelian groups is a Cayley graph. In this paper, we prove that every finite non-abelian group admits a non-Cayley Haar graph ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04551","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.04551","created_at":"2026-07-04T23:55:14.694281+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.04551v1","created_at":"2026-07-04T23:55:14.694281+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04551","created_at":"2026-07-04T23:55:14.694281+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPUWGJ3NO6A7","created_at":"2026-07-04T23:55:14.694281+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPUWGJ3NO6A72CC7","created_at":"2026-07-04T23:55:14.694281+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPUWGJ3N","created_at":"2026-07-04T23:55:14.694281+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/VPUWGJ3NO6A72CC7OAX4DNX7ZT","json":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT.json","graph_json":"https://pith.science/api/pith-number/VPUWGJ3NO6A72CC7OAX4DNX7ZT/graph.json","events_json":"https://pith.science/api/pith-number/VPUWGJ3NO6A72CC7OAX4DNX7ZT/events.json","paper":"https://pith.science/paper/VPUWGJ3N"},"agent_actions":{"view_html":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT","download_json":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT.json","view_paper":"https://pith.science/paper/VPUWGJ3N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.04551&json=true","fetch_graph":"https://pith.science/api/pith-number/VPUWGJ3NO6A72CC7OAX4DNX7ZT/graph.json","fetch_events":"https://pith.science/api/pith-number/VPUWGJ3NO6A72CC7OAX4DNX7ZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT/action/storage_attestation","attest_author":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT/action/author_attestation","sign_citation":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT/action/citation_signature","submit_replication":"https://pith.science/pith/VPUWGJ3NO6A72CC7OAX4DNX7ZT/action/replication_record"}},"created_at":"2026-07-04T23:55:14.694281+00:00","updated_at":"2026-07-04T23:55:14.694281+00:00"}