{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5ZGY7RVIQ67VCWZ6RL256BZG7C","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":"101747db4b5d73ee2f78a2b1556b5f3d53b54f24b6b488c5f976db30bdec08d7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T19:43:51Z","title_canon_sha256":"9d96772a21c8e089d8640bd4a28d321ca21a431315d687ae01c538fd70ea4be9"},"schema_version":"1.0","source":{"id":"1602.02297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02297","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02297v1","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02297","created_at":"2026-05-18T01:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"5ZGY7RVIQ67V","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5ZGY7RVIQ67VCWZ6","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5ZGY7RVI","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:215bd3f18fb76639488afb2fa9219fe8c650e63c3ce9e44cad166259ef3dea51","target":"graph","created_at":"2026-05-18T01:21:10Z","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":"In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is very restricted. It is described in Theorem~\\ref{111015a} where a short list of possible candidates for CIM-groups is given. Theorem~\\ref{111015c} provides concrete examples of infinite series of CIM-groups.","authors_text":"G\\'abor Somlai, Mikhail Muzychuk","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T19:43:51Z","title":"The Cayley isomorphism property for Cayley maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02297","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:b5d5ceda6fb8efd11de290642c47f4c342b06f238e7f56e3bcc7186a3d2f961b","target":"record","created_at":"2026-05-18T01:21:10Z","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":"101747db4b5d73ee2f78a2b1556b5f3d53b54f24b6b488c5f976db30bdec08d7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T19:43:51Z","title_canon_sha256":"9d96772a21c8e089d8640bd4a28d321ca21a431315d687ae01c538fd70ea4be9"},"schema_version":"1.0","source":{"id":"1602.02297","kind":"arxiv","version":1}},"canonical_sha256":"ee4d8fc6a887bf515b3e8af5df0726f8b6bc9d277b27ec81333604c418c31591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee4d8fc6a887bf515b3e8af5df0726f8b6bc9d277b27ec81333604c418c31591","first_computed_at":"2026-05-18T01:21:10.391160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:10.391160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x0wprSX5pK0x3TcixGAd8dDFZZ2NMx9CrGtbIqRiKvVsDiiTavinXXJ3vMU/N9mmMmdNOkTdFX9bGEAMesSACA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:10.391902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5d5ceda6fb8efd11de290642c47f4c342b06f238e7f56e3bcc7186a3d2f961b","sha256:215bd3f18fb76639488afb2fa9219fe8c650e63c3ce9e44cad166259ef3dea51"],"state_sha256":"53120e6b86d34825cd0b4161798cd345fcc33a5c3ff4b5b624ae0d21cfb77499"}