{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B2WXEVHUFPYVKDWSD7SITKPPDF","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":"1463fbb58b886957e9aa206137dbd82dd4507e4bf1366dec11cf65a2bad24c1e","cross_cats_sorted":["math.DS","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-15T20:15:08Z","title_canon_sha256":"ade50c0a6b0aad67435edde8591a1fa9db703842a6dc13100bd9fb18cdbadec3"},"schema_version":"1.0","source":{"id":"2607.14343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14343","created_at":"2026-07-17T00:21:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14343v1","created_at":"2026-07-17T00:21:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14343","created_at":"2026-07-17T00:21:06Z"},{"alias_kind":"pith_short_12","alias_value":"B2WXEVHUFPYV","created_at":"2026-07-17T00:21:06Z"},{"alias_kind":"pith_short_16","alias_value":"B2WXEVHUFPYVKDWS","created_at":"2026-07-17T00:21:06Z"},{"alias_kind":"pith_short_8","alias_value":"B2WXEVHU","created_at":"2026-07-17T00:21:06Z"}],"graph_snapshots":[{"event_id":"sha256:e83d9f5d2f204c2b9e3eddca9a0b6d554a0dbfbc4afa5a3bd68c396e98de9f1e","target":"graph","created_at":"2026-07-17T00:21:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.14343/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a mixed quantum Ising-$XY$ model on the semi-infinite rooted Cayley tree of order two. For every vertex $u$, the edge $\\langle u,(u,1)\\rangle$ carries an $XY$ interaction and the edge $\\langle u,(u,2)\\rangle$ carries an Ising interaction. Using the compatibility criterion for tree-indexed quantum Markov chains and consistently working with the normalized trace, we derive the translation-invariant boundary equation and compute explicitly the associated local transfer operator, namely the one-step partial-trace map which propagates successor boundary data to the parent vertex. We prove ","authors_text":"Farrukh Mukhamedov","cross_cats":["math.DS","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-15T20:15:08Z","title":"Quantum Markov Chains for an Asymmetric Mixed Ising-XY Model on a Cayley Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14343","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":"sha256:70b3dba810860b471e2faaa75d33bf5b831c7c24835bf3b5d744ca1e4a45319a","target":"record","created_at":"2026-07-17T00:21:06Z","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":"1463fbb58b886957e9aa206137dbd82dd4507e4bf1366dec11cf65a2bad24c1e","cross_cats_sorted":["math.DS","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-15T20:15:08Z","title_canon_sha256":"ade50c0a6b0aad67435edde8591a1fa9db703842a6dc13100bd9fb18cdbadec3"},"schema_version":"1.0","source":{"id":"2607.14343","kind":"arxiv","version":1}},"canonical_sha256":"0ead7254f42bf1550ed21fe489a9ef19604290b3de23890926e6f9835e2c2734","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ead7254f42bf1550ed21fe489a9ef19604290b3de23890926e6f9835e2c2734","first_computed_at":"2026-07-17T00:21:06.486284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T00:21:06.486284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9hEP4F1qU+1bEdt6pRXaf5/cITC3/HIkCcFdA9do0ekReVRsms582CtDuNo4tH8tLYbEHFllQjHSlzUw1WF6Aw==","signature_status":"signed_v1","signed_at":"2026-07-17T00:21:06.487115Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70b3dba810860b471e2faaa75d33bf5b831c7c24835bf3b5d744ca1e4a45319a","sha256:e83d9f5d2f204c2b9e3eddca9a0b6d554a0dbfbc4afa5a3bd68c396e98de9f1e"],"state_sha256":"051722d584d686004f14eccd0215b62fed9d813e38d37137c8f2783783ef6b60"}