{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D77D24OKFQXNMANZAWWT5V25ON","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":"bfa17464b3b86b53aa24117f60d8ab7a18384b1bd6205ef772455c7208c26641","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-09T20:37:38Z","title_canon_sha256":"7352871c470ee8b20fa17d1bca1e21b850d6a8fd2e89a3ef825fb296658359d1"},"schema_version":"1.0","source":{"id":"1304.2791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2791","created_at":"2026-05-18T01:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2791v1","created_at":"2026-05-18T01:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2791","created_at":"2026-05-18T01:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"D77D24OKFQXN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D77D24OKFQXNMANZ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D77D24OK","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:50687e1e66e2c13e0b22d53686999deb108a4d44fba56f89c2a269204e92e1fc","target":"graph","created_at":"2026-05-18T01:50:40Z","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":"We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature $\\beta$ and the interaction strength $K$. The rates of convergence results are obtained as $(\\beta,K)$ converges along appropriate sequences $(\\beta_n,K_n)$ to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein's method for normal and ","authors_text":"Bastian Martschink, Peter Eichelsbacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-09T20:37:38Z","title":"Phase transitions for rates of convergence in the Blume-Emery-Griffiths model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2791","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":"sha256:8183ed00a2542df72e11368274d46557cc27c06d7feb3adbc45c82446ca27d35","target":"record","created_at":"2026-05-18T01:50:40Z","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":"bfa17464b3b86b53aa24117f60d8ab7a18384b1bd6205ef772455c7208c26641","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-09T20:37:38Z","title_canon_sha256":"7352871c470ee8b20fa17d1bca1e21b850d6a8fd2e89a3ef825fb296658359d1"},"schema_version":"1.0","source":{"id":"1304.2791","kind":"arxiv","version":1}},"canonical_sha256":"1ffe3d71ca2c2ed601b905ad3ed75d7369d6da78a148a8b3747cf62729b759c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ffe3d71ca2c2ed601b905ad3ed75d7369d6da78a148a8b3747cf62729b759c7","first_computed_at":"2026-05-18T01:50:40.768857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:40.768857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"50s4Y0AzqTI9fI07XtqZK8e4y1wtSv0QA3Pmtemwij3fwhoKAZ/yiTHDRDz+ehNZzUToR3E8bnlqcXNSmvQiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:40.769626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8183ed00a2542df72e11368274d46557cc27c06d7feb3adbc45c82446ca27d35","sha256:50687e1e66e2c13e0b22d53686999deb108a4d44fba56f89c2a269204e92e1fc"],"state_sha256":"0aed4cca3e0ef868bad90a56cfca5c56d2f27492938af8740e1c7374ca20e35e"}