{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ILX7INCQ45NX4CMXICMSZ3I6XD","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":"a06140c95780954c6143d096a81e836dc2e65b2eb1b575b035a6252fbd871077","cross_cats_sorted":["math.DS","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-12T02:20:25Z","title_canon_sha256":"ebf3095685e0290b1ae62619d5ff9e69ecb5e2f42f814d4333838c13883b3fcf"},"schema_version":"1.0","source":{"id":"1204.2603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2603","created_at":"2026-05-18T03:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2603v1","created_at":"2026-05-18T03:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2603","created_at":"2026-05-18T03:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"ILX7INCQ45NX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"ILX7INCQ45NX4CMX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"ILX7INCQ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:0f47661170be3431ccc4703747cc05209269ef8b2154b4ee9ddd8e86ace959f4","target":"graph","created_at":"2026-05-18T03:48:44Z","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 the present paper we provide a new construction of measure, called $p$-adic quasi Gibbs measure, for countable state of $p$-adic Potts model on the Cayley tree. Such a construction depends on a parameter $\\frak{p}$ and wights. In particular case, i.e. if $\\frak{p}=\\exp_p$, the defined measure coincides with $p$-adic Gibbs measure. In this paper, under some condition on weights we establish the existence of $p$-adic quasi Gibbs measures associated with the model. Note that this condition does not depend on values of the prime $p$. An analogues fact is not valid when the number of spins is fi","authors_text":"Farrukh Mukhamedov","cross_cats":["math.DS","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-12T02:20:25Z","title":"Existence of $P$-adic quasi Gibbs measure for countable state Potts model on the Cayley tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2603","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:da7dab604717df400f4c146f40138681c520370031a893df9664b7ebc6d1395b","target":"record","created_at":"2026-05-18T03:48:44Z","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":"a06140c95780954c6143d096a81e836dc2e65b2eb1b575b035a6252fbd871077","cross_cats_sorted":["math.DS","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-12T02:20:25Z","title_canon_sha256":"ebf3095685e0290b1ae62619d5ff9e69ecb5e2f42f814d4333838c13883b3fcf"},"schema_version":"1.0","source":{"id":"1204.2603","kind":"arxiv","version":1}},"canonical_sha256":"42eff43450e75b7e099740992ced1eb8c3262bf886b86baf66dcff4983c83850","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42eff43450e75b7e099740992ced1eb8c3262bf886b86baf66dcff4983c83850","first_computed_at":"2026-05-18T03:48:44.905628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:44.905628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEK1eGA59xfRzcGLgAsjdW7NdvbtFkzWujxxJDSUSgZ95DbsQSCh8n0P2b19qEef+lKM178yRcBCk+t6VPXOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:44.906145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7dab604717df400f4c146f40138681c520370031a893df9664b7ebc6d1395b","sha256:0f47661170be3431ccc4703747cc05209269ef8b2154b4ee9ddd8e86ace959f4"],"state_sha256":"fa1dba2f5c002964798936ec3d132560e415bd037e60ecb989c1fddeedee0695"}