{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RZXE4WYFL3FMWUEQHWKVOVZ2BE","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":"8f515be6b956bb3bf7a59f05a4925b9deecaf3888d1043feb7c1cc6c69e854d9","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-01-25T10:04:55Z","title_canon_sha256":"3018b2773d2aab85d2bdee2a1fa84f4bcdae0423deaf90d27dc69d4abe94c206"},"schema_version":"1.0","source":{"id":"2201.10209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.10209","created_at":"2026-07-05T03:51:16Z"},{"alias_kind":"arxiv_version","alias_value":"2201.10209v1","created_at":"2026-07-05T03:51:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.10209","created_at":"2026-07-05T03:51:16Z"},{"alias_kind":"pith_short_12","alias_value":"RZXE4WYFL3FM","created_at":"2026-07-05T03:51:16Z"},{"alias_kind":"pith_short_16","alias_value":"RZXE4WYFL3FMWUEQ","created_at":"2026-07-05T03:51:16Z"},{"alias_kind":"pith_short_8","alias_value":"RZXE4WYF","created_at":"2026-07-05T03:51:16Z"}],"graph_snapshots":[{"event_id":"sha256:985272e75ec7d70e123f44d59db7c19bc9b5ea31529fcdb796ba00e38a4b75e8","target":"graph","created_at":"2026-07-05T03:51:16Z","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/2201.10209/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.","authors_text":"Hjalmar Rosengren, Jakob Bj\\\"ornberg, Kieran Ryan","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-01-25T10:04:55Z","title":"Heisenberg models and Schur--Weyl duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.10209","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":"sha256:1f3c52d83f11fad8c9a5b5d8710bfee7f44624f60ac37e0124f50de1113ecc8e","target":"record","created_at":"2026-07-05T03:51:16Z","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":"8f515be6b956bb3bf7a59f05a4925b9deecaf3888d1043feb7c1cc6c69e854d9","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-01-25T10:04:55Z","title_canon_sha256":"3018b2773d2aab85d2bdee2a1fa84f4bcdae0423deaf90d27dc69d4abe94c206"},"schema_version":"1.0","source":{"id":"2201.10209","kind":"arxiv","version":1}},"canonical_sha256":"8e6e4e5b055ecacb50903d9557573a09321c7271e1f742b58780119413c5bf4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6e4e5b055ecacb50903d9557573a09321c7271e1f742b58780119413c5bf4e","first_computed_at":"2026-07-05T03:51:16.730224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:51:16.730224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vlPdy6eC+Ht0BFE8oMrtTr8lXCV5YZoudi+nbh2fFSNioR/AlqnFW439O2NFqGbRnb7vK1K8UquWUcXq5y+uAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:51:16.730647Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.10209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f3c52d83f11fad8c9a5b5d8710bfee7f44624f60ac37e0124f50de1113ecc8e","sha256:985272e75ec7d70e123f44d59db7c19bc9b5ea31529fcdb796ba00e38a4b75e8"],"state_sha256":"6c89d1529001ae58e928ed1fb2bdb2f7a72ab624c6675db911b6ecd4b59f4059"}