{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N3DOP3WMQ4AVB57DNG4R5HVV7I","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":"5921bd9acc6104c6872fa70042fbbe0697722fa9a86629f07c08c6088b77e213","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-12T03:33:10Z","title_canon_sha256":"8ad1076e662d194d90ac3e5b84853f83bc90326ef40857885d3627ec4408df4b"},"schema_version":"1.0","source":{"id":"1510.03129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03129","created_at":"2026-05-18T01:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03129v1","created_at":"2026-05-18T01:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03129","created_at":"2026-05-18T01:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"N3DOP3WMQ4AV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N3DOP3WMQ4AVB57D","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N3DOP3WM","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:6be27ec6fa72f2e5ad0b352a0bff4cfc8a6fb3b9a25119b8b69bc3092738a79b","target":"graph","created_at":"2026-05-18T01:29:40Z","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 continue an investigation of the $p$-adic Ising-Vannimenus model on the Cayley tree of an arbitrary order $k$ $(k\\geq 2$). We prove the existence of $p$-adic quasi Gibbs measures by analyzing fixed points of multi-dimensional $p$-adic system of equations. We are also able to show the uniqueness of translation-invariant $p$-adic Gibbs measure. Finally, it is established the existence of the phase transition for the Ising-Vannimenus model depending on the order $k$ of the Cayley tree and the prime $p$. Note that the methods used in the paper are not valid in the real setting, s","authors_text":"Farrukh Mukhamedov, Mansoor Saburov, Otabek Khakimov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-12T03:33:10Z","title":"On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03129","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:b21d5cb007a2f9048799e060ffe1074b6a8986171de87b8ede4d6afc4e847d89","target":"record","created_at":"2026-05-18T01:29:40Z","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":"5921bd9acc6104c6872fa70042fbbe0697722fa9a86629f07c08c6088b77e213","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-12T03:33:10Z","title_canon_sha256":"8ad1076e662d194d90ac3e5b84853f83bc90326ef40857885d3627ec4408df4b"},"schema_version":"1.0","source":{"id":"1510.03129","kind":"arxiv","version":1}},"canonical_sha256":"6ec6e7eecc870150f7e369b91e9eb5fa3ba983aa26607206f4ec64f52809eb77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ec6e7eecc870150f7e369b91e9eb5fa3ba983aa26607206f4ec64f52809eb77","first_computed_at":"2026-05-18T01:29:40.233195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:40.233195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T91lSWKyFtnAU07ilH5Q7cVQnvy/7W3dcUNg6cncvUId9rxLDaFCcyIsmIBi/s0iktSzlPjHJB4RNny4Ry6IAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:40.233933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b21d5cb007a2f9048799e060ffe1074b6a8986171de87b8ede4d6afc4e847d89","sha256:6be27ec6fa72f2e5ad0b352a0bff4cfc8a6fb3b9a25119b8b69bc3092738a79b"],"state_sha256":"95fc27916c6a2619384e68bae6ef1d6b987173daf22d4a2adb92f63fb2398aa1"}