{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:R5FNKRQME2SKMMNNEAQNZEAPR4","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":"a8552694453c68657f21062f8cbe4339a76810ab4ee0ff275ed3507aa90db2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-14T06:34:44Z","title_canon_sha256":"18a920cb4d95616b3f45390bbdcb56802a5d59a50a14f48e6752e710d96c16d8"},"schema_version":"1.0","source":{"id":"0904.2057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2057","created_at":"2026-05-18T02:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2057v1","created_at":"2026-05-18T02:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2057","created_at":"2026-05-18T02:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"R5FNKRQME2SK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"R5FNKRQME2SKMMNN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"R5FNKRQM","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:a06a69d13c1dfae485049f3372e907b83862dd04726bf307daaeee634c0422fd","target":"graph","created_at":"2026-05-18T02:14:06Z","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 define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs (complete cycle, complete $","authors_text":"M. A. Jafarizadeh, S. Salimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-14T06:34:44Z","title":"Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2057","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":"sha256:1b401599ea76558e16b864907d99fc04edebd793b3a04ef07d53134967707fdc","target":"record","created_at":"2026-05-18T02:14:06Z","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":"a8552694453c68657f21062f8cbe4339a76810ab4ee0ff275ed3507aa90db2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-14T06:34:44Z","title_canon_sha256":"18a920cb4d95616b3f45390bbdcb56802a5d59a50a14f48e6752e710d96c16d8"},"schema_version":"1.0","source":{"id":"0904.2057","kind":"arxiv","version":1}},"canonical_sha256":"8f4ad5460c26a4a631ad2020dc900f8f2ac30c7cc93146bb19bec05e00469cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f4ad5460c26a4a631ad2020dc900f8f2ac30c7cc93146bb19bec05e00469cdf","first_computed_at":"2026-05-18T02:14:06.128719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:06.128719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k3wxV4ax/Pv1+9uKPjBFmE5RkcVLRuv2afiEj/jnBXLNf9QXb1975eP3aqb0vYQzpkdZvsnrlJoIKWDIVB3uDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:06.129166Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b401599ea76558e16b864907d99fc04edebd793b3a04ef07d53134967707fdc","sha256:a06a69d13c1dfae485049f3372e907b83862dd04726bf307daaeee634c0422fd"],"state_sha256":"d1cc42356b2443d51fba766b4ccfa7af2eca5c74ab0447812ff68a7d5ec67aff"}