{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7GZHZC4EHOSBO4KBYGJFPJULPI","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":"6c3e70bfcfd9618854b41eb3a5f2d676f95ad9767c6f16a8e497ffd287fb3a20","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-10-06T14:12:22Z","title_canon_sha256":"ddb3d173a66eaba4e977d29e484b935243f5fafafe1af70a085cea9e337ea49d"},"schema_version":"1.0","source":{"id":"math-ph/0510024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0510024","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0510024v2","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0510024","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"7GZHZC4EHOSB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7GZHZC4EHOSBO4KB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7GZHZC4E","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:780ec9b5e0a3f7ba05edadd72a6b8cf1fe5ee9b5ac1eb9cf3b069abacf30d9d9","target":"graph","created_at":"2026-05-18T02:35:38Z","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":"We consider a nearest-neighbor inhomogeneous $p$-adic Potts (with $q\\geq 2$ spin values) model on the Cayley tree of order $k\\geq 1$. The inhomogeneity means that the interaction $J_{xy}$ couplings depend on nearest-neighbors points $x, y $ of the Cayley tree. We study ($p-$ adic) Gibbs measures of the model. We show that (i) if $q\\notin p\\mathbb{N}$ then there is unique Gibbs measure for any $k\\geq 1$ and $\\forall J_{xy}$ with $|J_{xy}|<p^{-1/(p-1)}$. (ii) For $q\\in p\\mathbb{N}, p\\geq 3$ one can choose $J_{xy}$ and $k\\geq 1$ such that there exist at least two Gibbs measures which are translat","authors_text":"Farrukh Mukhamedov, Utkir Rozikov","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-10-06T14:12:22Z","title":"On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510024","kind":"arxiv","version":2},"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:bbf0d29287a25caa9de57fe318001ab755fa3d62c55922bff5a179bb172ee90a","target":"record","created_at":"2026-05-18T02:35:38Z","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":"6c3e70bfcfd9618854b41eb3a5f2d676f95ad9767c6f16a8e497ffd287fb3a20","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-10-06T14:12:22Z","title_canon_sha256":"ddb3d173a66eaba4e977d29e484b935243f5fafafe1af70a085cea9e337ea49d"},"schema_version":"1.0","source":{"id":"math-ph/0510024","kind":"arxiv","version":2}},"canonical_sha256":"f9b27c8b843ba4177141c19257a68b7a0bec64ff711bd320373ab2d5d0541494","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9b27c8b843ba4177141c19257a68b7a0bec64ff711bd320373ab2d5d0541494","first_computed_at":"2026-05-18T02:35:38.685001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.685001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FSZEdsuPyX6d+JuAYR1szsM5QCI0CHdWgSrP5FiS7IXWC6T9C7Gskv5USbOfSwnxH9JqfYtqlBKgXLw3TZrsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.685417Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0510024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbf0d29287a25caa9de57fe318001ab755fa3d62c55922bff5a179bb172ee90a","sha256:780ec9b5e0a3f7ba05edadd72a6b8cf1fe5ee9b5ac1eb9cf3b069abacf30d9d9"],"state_sha256":"27a44a3db35d097888ec547782608418df52827f85bca6865b235e2444528f94"}