{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IQTM4UWYAGMZS3VC7DJ3PVQYBI","short_pith_number":"pith:IQTM4UWY","schema_version":"1.0","canonical_sha256":"4426ce52d80199996ea2f8d3b7d6180a27d8ff7437f6451488cbc5fe6cc250b4","source":{"kind":"arxiv","id":"1011.2256","version":1},"attestation_state":"computed","paper":{"title":"On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Farrukh Mukhamedov, Luigi Accardi, Mansoor Saburov","submitted_at":"2010-11-10T01:51:12Z","abstract_excerpt":"In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\\{K_{<x,y>}\\}$."},"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":"1011.2256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-10T01:51:12Z","cross_cats_sorted":["math.DS","math.FA","math.MP","math.OA","quant-ph"],"title_canon_sha256":"b971f0a3bf0341d0ca39c42dfb7a83394fa4862c18bbf81d87978518e5e3ffb8","abstract_canon_sha256":"2d75e9fc90df068f612e8f9a8627529639c764d4571fe1e837641ebf6f0ebf22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:06.900922Z","signature_b64":"YKAi9tdwVcT0owaRHl6AjyYty1/cIRZf/ywZiFqxlYLO8IDFgN7Z+TMx3ttH7a5Hn16BjQPYAVaBu30PAV3/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4426ce52d80199996ea2f8d3b7d6180a27d8ff7437f6451488cbc5fe6cc250b4","last_reissued_at":"2026-05-18T04:04:06.900458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:06.900458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Farrukh Mukhamedov, Luigi Accardi, Mansoor Saburov","submitted_at":"2010-11-10T01:51:12Z","abstract_excerpt":"In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\\{K_{<x,y>}\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2256","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":"1011.2256","created_at":"2026-05-18T04:04:06.900518+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2256v1","created_at":"2026-05-18T04:04:06.900518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2256","created_at":"2026-05-18T04:04:06.900518+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQTM4UWYAGMZ","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQTM4UWYAGMZS3VC","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQTM4UWY","created_at":"2026-05-18T12:26:09.077623+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/IQTM4UWYAGMZS3VC7DJ3PVQYBI","json":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI.json","graph_json":"https://pith.science/api/pith-number/IQTM4UWYAGMZS3VC7DJ3PVQYBI/graph.json","events_json":"https://pith.science/api/pith-number/IQTM4UWYAGMZS3VC7DJ3PVQYBI/events.json","paper":"https://pith.science/paper/IQTM4UWY"},"agent_actions":{"view_html":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI","download_json":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI.json","view_paper":"https://pith.science/paper/IQTM4UWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2256&json=true","fetch_graph":"https://pith.science/api/pith-number/IQTM4UWYAGMZS3VC7DJ3PVQYBI/graph.json","fetch_events":"https://pith.science/api/pith-number/IQTM4UWYAGMZS3VC7DJ3PVQYBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI/action/storage_attestation","attest_author":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI/action/author_attestation","sign_citation":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI/action/citation_signature","submit_replication":"https://pith.science/pith/IQTM4UWYAGMZS3VC7DJ3PVQYBI/action/replication_record"}},"created_at":"2026-05-18T04:04:06.900518+00:00","updated_at":"2026-05-18T04:04:06.900518+00:00"}