{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:R5FNKRQME2SKMMNNEAQNZEAPR4","short_pith_number":"pith:R5FNKRQM","schema_version":"1.0","canonical_sha256":"8f4ad5460c26a4a631ad2020dc900f8f2ac30c7cc93146bb19bec05e00469cdf","source":{"kind":"arxiv","id":"0904.2057","version":1},"attestation_state":"computed","paper":{"title":"Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"M. A. Jafarizadeh, S. Salimi","submitted_at":"2009-04-14T06:34:44Z","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 $"},"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":"0904.2057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-14T06:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"18a920cb4d95616b3f45390bbdcb56802a5d59a50a14f48e6752e710d96c16d8","abstract_canon_sha256":"a8552694453c68657f21062f8cbe4339a76810ab4ee0ff275ed3507aa90db2cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:06.129166Z","signature_b64":"k3wxV4ax/Pv1+9uKPjBFmE5RkcVLRuv2afiEj/jnBXLNf9QXb1975eP3aqb0vYQzpkdZvsnrlJoIKWDIVB3uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f4ad5460c26a4a631ad2020dc900f8f2ac30c7cc93146bb19bec05e00469cdf","last_reissued_at":"2026-05-18T02:14:06.128719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:06.128719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"M. A. Jafarizadeh, S. Salimi","submitted_at":"2009-04-14T06:34:44Z","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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2057","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":""},"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":"0904.2057","created_at":"2026-05-18T02:14:06.128781+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.2057v1","created_at":"2026-05-18T02:14:06.128781+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2057","created_at":"2026-05-18T02:14:06.128781+00:00"},{"alias_kind":"pith_short_12","alias_value":"R5FNKRQME2SK","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"R5FNKRQME2SKMMNN","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"R5FNKRQM","created_at":"2026-05-18T12:26:01.383474+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/R5FNKRQME2SKMMNNEAQNZEAPR4","json":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4.json","graph_json":"https://pith.science/api/pith-number/R5FNKRQME2SKMMNNEAQNZEAPR4/graph.json","events_json":"https://pith.science/api/pith-number/R5FNKRQME2SKMMNNEAQNZEAPR4/events.json","paper":"https://pith.science/paper/R5FNKRQM"},"agent_actions":{"view_html":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4","download_json":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4.json","view_paper":"https://pith.science/paper/R5FNKRQM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.2057&json=true","fetch_graph":"https://pith.science/api/pith-number/R5FNKRQME2SKMMNNEAQNZEAPR4/graph.json","fetch_events":"https://pith.science/api/pith-number/R5FNKRQME2SKMMNNEAQNZEAPR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4/action/storage_attestation","attest_author":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4/action/author_attestation","sign_citation":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4/action/citation_signature","submit_replication":"https://pith.science/pith/R5FNKRQME2SKMMNNEAQNZEAPR4/action/replication_record"}},"created_at":"2026-05-18T02:14:06.128781+00:00","updated_at":"2026-05-18T02:14:06.128781+00:00"}