{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R6SUIOE2K3YT4HRJPJZP7JA56X","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":"5971edf9122c698bb6609564e50078dd20bad4f552338a87384e0486b99f8b37","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T15:03:22Z","title_canon_sha256":"bb2edf0588a456595c2dcf1ce97aaae93cde40340bd189da71e6c78856c141f6"},"schema_version":"1.0","source":{"id":"1811.12834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12834","created_at":"2026-07-05T02:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12834v2","created_at":"2026-07-05T02:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12834","created_at":"2026-07-05T02:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"R6SUIOE2K3YT","created_at":"2026-07-05T02:52:55Z"},{"alias_kind":"pith_short_16","alias_value":"R6SUIOE2K3YT4HRJ","created_at":"2026-07-05T02:52:55Z"},{"alias_kind":"pith_short_8","alias_value":"R6SUIOE2","created_at":"2026-07-05T02:52:55Z"}],"graph_snapshots":[{"event_id":"sha256:83e4e4d769d7e1a57c59832601f1406d59eb1aaf7603dfc1e1869f5bd23ad40a","target":"graph","created_at":"2026-07-05T02:52:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.12834/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of Poisson--Dirichlet distributions.","authors_text":"Daniel Ueltschi, Jakob E. Bj\\\"ornberg, J\\\"urg Fr\\\"ohlich","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T15:03:22Z","title":"Quantum spins and random loops on the complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12834","kind":"arxiv","version":2},"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":"sha256:0f41190eefd001769562f0faa3261d335afd3e27e0469dc69d25ea6de166bab3","target":"record","created_at":"2026-07-05T02:52:55Z","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":"5971edf9122c698bb6609564e50078dd20bad4f552338a87384e0486b99f8b37","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T15:03:22Z","title_canon_sha256":"bb2edf0588a456595c2dcf1ce97aaae93cde40340bd189da71e6c78856c141f6"},"schema_version":"1.0","source":{"id":"1811.12834","kind":"arxiv","version":2}},"canonical_sha256":"8fa544389a56f13e1e297a72ffa41df5f0761a6c76a30f374310fe7eb01d4918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fa544389a56f13e1e297a72ffa41df5f0761a6c76a30f374310fe7eb01d4918","first_computed_at":"2026-07-05T02:52:55.522588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:52:55.522588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssyUQZffemzZMj0BZK2LkOMCxIRChan+RYHMV4ON5sxlHUE6ObAGZMvkoGiOr7L2kEw5K7dzsO5l3i9Jt6R5Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:52:55.523082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f41190eefd001769562f0faa3261d335afd3e27e0469dc69d25ea6de166bab3","sha256:83e4e4d769d7e1a57c59832601f1406d59eb1aaf7603dfc1e1869f5bd23ad40a"],"state_sha256":"cbb09219bc3c982e2d904cbac452f560254cbe79ff9735af2291e02afe9086d2"}