{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VPUWGJ3NO6A72CC7OAX4DNX7ZT","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":"a8dcc835a8419c8e390bd0b6937b6835cc125857326c8fc007787e36c4334ac7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-13T09:06:16Z","title_canon_sha256":"a3934f1f80f877b8c71ade6fd6d056cecf7ee6888de1e84b0fce0efec372df4e"},"schema_version":"1.0","source":{"id":"1908.04551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04551","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04551v1","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04551","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"VPUWGJ3NO6A7","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_16","alias_value":"VPUWGJ3NO6A72CC7","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_8","alias_value":"VPUWGJ3N","created_at":"2026-07-04T23:55:14Z"}],"graph_snapshots":[{"event_id":"sha256:bc66ab0d614491ec972de489717b354540aaa5f310434925243bf9a9620abb0d","target":"graph","created_at":"2026-07-04T23:55:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04551/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Da-Wei Yang, Istv\\'an Kov\\'acs, Jie Wang, Yan-Quan Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-13T09:06:16Z","title":"Existence of non-Cayley Haar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04551","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":"sha256:25cc10652fa5d62c3451137443b5d05b5e6eaeff16a9141ffaabbeb77f1fa218","target":"record","created_at":"2026-07-04T23:55:14Z","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":"a8dcc835a8419c8e390bd0b6937b6835cc125857326c8fc007787e36c4334ac7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-13T09:06:16Z","title_canon_sha256":"a3934f1f80f877b8c71ade6fd6d056cecf7ee6888de1e84b0fce0efec372df4e"},"schema_version":"1.0","source":{"id":"1908.04551","kind":"arxiv","version":1}},"canonical_sha256":"abe963276d7781fd085f702fc1b6ffcce141154228e980cec5af3aaed028b464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe963276d7781fd085f702fc1b6ffcce141154228e980cec5af3aaed028b464","first_computed_at":"2026-07-04T23:55:14.694223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:14.694223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5GPNl6+TZl99sk4k88fIBL1Y2pRIXJ2ngGsmXuXl9iWyXvO9tj1cXouLaBfLHFa7PZuEv+1PDu6ESHBeGw81BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:14.694592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25cc10652fa5d62c3451137443b5d05b5e6eaeff16a9141ffaabbeb77f1fa218","sha256:bc66ab0d614491ec972de489717b354540aaa5f310434925243bf9a9620abb0d"],"state_sha256":"945b6b0a5c0a327af2b522dddd801b1d0d2204afa8fe2981e4309d53c04900e0"}