{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NEVJSTM4AKHAYDJCQFJQH3TCLH","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":"2212e790a615838112b86c1fd13fda954b663b93a83a822a077dbc22f5edd453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-07T15:06:31Z","title_canon_sha256":"7ae576355dfff8186b05ecd2d7e3c4f82f19aafddd18e6373dca5dc7ecd780f1"},"schema_version":"1.0","source":{"id":"1708.02152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02152","created_at":"2026-05-18T00:38:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02152v1","created_at":"2026-05-18T00:38:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02152","created_at":"2026-05-18T00:38:31Z"},{"alias_kind":"pith_short_12","alias_value":"NEVJSTM4AKHA","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NEVJSTM4AKHAYDJC","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NEVJSTM4","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:acfbf549eb76a24225f69e7dcf7f39c5aa45eeece5aae59846e432505fcec24e","target":"graph","created_at":"2026-05-18T00:38:31Z","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 study the set of $p$-adic Gibbs measures of the $q$-states Potts model on the Cayley tree of order three. We prove the vastness of the periodic $p$-adic Gibbs measures for such model by showing the chaotic behavior of the correspondence Potts--Bethe mapping over $\\mathbb{Q}\\_p$ for $p\\equiv 1 \\ (\\rm{mod} \\ 3)$. In fact, for $0 < |\\theta-1|\\_p < |q|\\_p^2 < 1$, there exists a subsystem that isometrically conjugate to the full shift on three symbols. Meanwhile, for $0 < |q|\\_p^2 \\leq |\\theta-1|\\_p < |q|\\_p < 1$, there exists a subsystem that isometrically conjugate to a subshift of finite type","authors_text":"Lingmin Liao (LAMA), Mansoor Saburov, Mohd Ali Khameini Ahmad (LAMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-07T15:06:31Z","title":"Periodic $p$-adic Gibbs measures of $q$-states Potts model on Cayley tree: The chaos implies the vastness of $p$-adic Gibbs measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02152","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":"sha256:651a00047a8c2f6d7a0350bae36afb1cf4c219303a58cd87d28bd03b2400416e","target":"record","created_at":"2026-05-18T00:38:31Z","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":"2212e790a615838112b86c1fd13fda954b663b93a83a822a077dbc22f5edd453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-07T15:06:31Z","title_canon_sha256":"7ae576355dfff8186b05ecd2d7e3c4f82f19aafddd18e6373dca5dc7ecd780f1"},"schema_version":"1.0","source":{"id":"1708.02152","kind":"arxiv","version":1}},"canonical_sha256":"692a994d9c028e0c0d22815303ee6259ea4d5cf747aeaab6ef50864410c2236b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"692a994d9c028e0c0d22815303ee6259ea4d5cf747aeaab6ef50864410c2236b","first_computed_at":"2026-05-18T00:38:31.922615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:31.922615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hBMfU1djsWQ8zhBbkAFF8yFclgt73zUw8suQtaP/vdjtcVjB4+n5awFlIj7xTc3xi/U7VXps5dIldo4U9S9zAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:31.923246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:651a00047a8c2f6d7a0350bae36afb1cf4c219303a58cd87d28bd03b2400416e","sha256:acfbf549eb76a24225f69e7dcf7f39c5aa45eeece5aae59846e432505fcec24e"],"state_sha256":"e79c2d4858f212b94a24e7ca7772f5e629e169cb459f708239e931eab2db479b"}