{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GWHXQN3TRGLPR43DDAOLAIQAA2","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":"b0cc7cab023e96707521a224e7888876da519cf5b4573f19ba95a823a1433dfb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T20:35:18Z","title_canon_sha256":"f5dc3f6c82ed92e1c4d458c078b1cd7183660281397f23d0a0cd7536187d8ee6"},"schema_version":"1.0","source":{"id":"1803.02867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02867","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02867v1","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02867","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"GWHXQN3TRGLP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWHXQN3TRGLPR43D","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWHXQN3T","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:b9609992a31dc979fb79f2b5e6cb2741ed14de7d28fcbbbdf02bdbbd81d5c701","target":"graph","created_at":"2026-05-18T00:21:45Z","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 complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in [EsHaRo12,EsRo10,BoEsRo13,JaKuBo14,Bo17]. The potential is of nearest-neighbor type and the local state space is compact but uncountable. Based on the system parameters we prove existence of a critical value $\\theta_{\\rm c}$ such that for $\\theta\\le \\theta_{\\rm c}$ there is a unique translation-invariant splitting Gibbs measure. For $\\theta_{\\rm c}<\\theta$ there is a phase transition with exactly three translation-invariant splitting Gibbs measures. The proof rests on an analysis o","authors_text":"Benedikt Jahnel, Golibjon Botirov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T20:35:18Z","title":"Phase transitions for a model with uncountable spin space on the Cayley tree: the general case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02867","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":"sha256:183a9db2e5ba001689210eba0ea9756f330526bb0283e97847c09e4dc464c5e2","target":"record","created_at":"2026-05-18T00:21:45Z","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":"b0cc7cab023e96707521a224e7888876da519cf5b4573f19ba95a823a1433dfb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T20:35:18Z","title_canon_sha256":"f5dc3f6c82ed92e1c4d458c078b1cd7183660281397f23d0a0cd7536187d8ee6"},"schema_version":"1.0","source":{"id":"1803.02867","kind":"arxiv","version":1}},"canonical_sha256":"358f7837738996f8f363181cb022000685ff781ef7d4c4b1661927c6ad7a996e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358f7837738996f8f363181cb022000685ff781ef7d4c4b1661927c6ad7a996e","first_computed_at":"2026-05-18T00:21:45.251084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:45.251084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AC+DYhGkOUAftDuE6+vrTJPSnRoAwYBfVg95yZZ4ZswfLrPCojst+VlrtR/x4XuUklnQW2x7c9RyPqbzRrWSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:45.251759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:183a9db2e5ba001689210eba0ea9756f330526bb0283e97847c09e4dc464c5e2","sha256:b9609992a31dc979fb79f2b5e6cb2741ed14de7d28fcbbbdf02bdbbd81d5c701"],"state_sha256":"f74366a655c5b50d1bbd16ef17844e45356761f25b6a62222a9165901a0e34a5"}