{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3R4PS6TIV6LZTUXCQC5EFYKLSO","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":"8b9856d8c620763d54f734baa0b5764239ad25eafc1a68e1660ba91b51af790f","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-08T01:36:41Z","title_canon_sha256":"bf94c25a2922699af5c34fff7c89f7f7bb7afe24bafdaac41d14dc8c245488a8"},"schema_version":"1.0","source":{"id":"1611.02356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02356","created_at":"2026-05-18T00:59:52Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02356v1","created_at":"2026-05-18T00:59:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02356","created_at":"2026-05-18T00:59:52Z"},{"alias_kind":"pith_short_12","alias_value":"3R4PS6TIV6LZ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3R4PS6TIV6LZTUXC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3R4PS6TI","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:e9e2d0208260857b3114deacd5b14a8261b33053b1707e14c44e63580dfe7f1e","target":"graph","created_at":"2026-05-18T00:59:52Z","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 discuss spin models on complete graphs in the mean-field (infinite-vertex) limit, especially the classical XY model, the Toy model of the Higgs sector, and related generalizations. We present a number of results coming from the theory of large deviations and Stein's method, in particular, Cram\\'er and Sanov-type results, limit theorems with rates of convergence, and phase transition behavior for these models.","authors_text":"Kay Kirkpatrick, Tayyab Nawaz","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-08T01:36:41Z","title":"Critical behavior of mean-field XY and related models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02356","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":"sha256:3c3864956715cc8369c8b7043df42ba90d5a2ac0f68564808afe9f45046bcb1b","target":"record","created_at":"2026-05-18T00:59:52Z","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":"8b9856d8c620763d54f734baa0b5764239ad25eafc1a68e1660ba91b51af790f","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-08T01:36:41Z","title_canon_sha256":"bf94c25a2922699af5c34fff7c89f7f7bb7afe24bafdaac41d14dc8c245488a8"},"schema_version":"1.0","source":{"id":"1611.02356","kind":"arxiv","version":1}},"canonical_sha256":"dc78f97a68af9799d2e280ba42e14b938f797fbe21a6f2fa2dae9aad07b56cf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc78f97a68af9799d2e280ba42e14b938f797fbe21a6f2fa2dae9aad07b56cf7","first_computed_at":"2026-05-18T00:59:52.310006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:52.310006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CurhRAZbMwxIhqJaVvuMTgFLDj16976H8KPVCc0g0xTQke+3g9KXbu1o/ntAyIpFTFue+tgLECpEMEaEwN51Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:52.310630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c3864956715cc8369c8b7043df42ba90d5a2ac0f68564808afe9f45046bcb1b","sha256:e9e2d0208260857b3114deacd5b14a8261b33053b1707e14c44e63580dfe7f1e"],"state_sha256":"ae7020e0d1af3f49a57302d66b7f87854e77e74d4878b330fb8d241d791436d8"}