{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AR77KVFUJ7IQGGGI6EZZXC6O5Q","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":"6b77cca611cf0a5a1b353e1d500d76967c4c877e7a7133ab87e37c90fd78ebbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-20T12:11:46Z","title_canon_sha256":"cac8215fd9d6ca68ee65f8bf31b4bdeffe6a0e10dbfe0797b3f468b7b7b8895f"},"schema_version":"1.0","source":{"id":"1402.4978","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4978","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4978v1","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4978","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"AR77KVFUJ7IQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AR77KVFUJ7IQGGGI","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AR77KVFU","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8dd34019bd6987eeb316fc9300c016db35c28263d77e06a7509498fe186c43a9","target":"graph","created_at":"2026-05-18T02:58:31Z","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, all finite groups whose commuting (non-commuting) graphs can be embed on the plane, torus or projective plane are classified.","authors_text":"Kazem Khashyarmanesh, Mohammad Farrokhi Derakhshandeh Ghouchan, Mojgan Afkhami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-20T12:11:46Z","title":"Toroidal and projective commuting and non-commuting graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4978","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:b80221d30dd35543cddc1f2725ce058b34b59abad1ce7f8c31b18c36e4326d2e","target":"record","created_at":"2026-05-18T02:58:31Z","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":"6b77cca611cf0a5a1b353e1d500d76967c4c877e7a7133ab87e37c90fd78ebbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-20T12:11:46Z","title_canon_sha256":"cac8215fd9d6ca68ee65f8bf31b4bdeffe6a0e10dbfe0797b3f468b7b7b8895f"},"schema_version":"1.0","source":{"id":"1402.4978","kind":"arxiv","version":1}},"canonical_sha256":"047ff554b44fd10318c8f1339b8bceec3989713c45599caaab8ce1a24486d8e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"047ff554b44fd10318c8f1339b8bceec3989713c45599caaab8ce1a24486d8e8","first_computed_at":"2026-05-18T02:58:31.470680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:31.470680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3aX9m/Mea26dQu1RSVC2UYWuqy5CDVXhROD62ujM8GEnJimzrHb4p045Ydn89MMBsLwizI0hPJCJEUo9dBZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:31.471391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4978","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b80221d30dd35543cddc1f2725ce058b34b59abad1ce7f8c31b18c36e4326d2e","sha256:8dd34019bd6987eeb316fc9300c016db35c28263d77e06a7509498fe186c43a9"],"state_sha256":"52ebfa3fad2c97db5583b787fdd30d6fbcaa643b26af2b6484c239d6c968f9c4"}