{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RAOO2XZTGHJEU342WRRPPUD2PJ","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":"46096d6d8f7b5a90788584fa8ed9a77d662d2d87c31a05b560c982dd6db50ad4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-12-01T18:06:48Z","title_canon_sha256":"5eaf1ae384d1c8d688dfdb1d5088f24885fb6e15babaffeaf824baa0e619ec17"},"schema_version":"1.0","source":{"id":"2512.01956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.01956","created_at":"2026-06-04T01:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"2512.01956v2","created_at":"2026-06-04T01:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.01956","created_at":"2026-06-04T01:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"RAOO2XZTGHJE","created_at":"2026-06-04T01:08:36Z"},{"alias_kind":"pith_short_16","alias_value":"RAOO2XZTGHJEU342","created_at":"2026-06-04T01:08:36Z"},{"alias_kind":"pith_short_8","alias_value":"RAOO2XZT","created_at":"2026-06-04T01:08:36Z"}],"graph_snapshots":[{"event_id":"sha256:3630f173ae55282fc22d5716d8922eeeaf89106209af0fbef4067003c803fc27","target":"graph","created_at":"2026-06-04T01:08:36Z","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/2512.01956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Algebraically decaying interactions $\\sim 1/r^{d+\\sigma}$ can lead to nontrivial universality beyond short-range (SR) theories and spontaneous symmetry breaking in low-dimensional systems. We perform large-scale Monte Carlo simulations for the classical long-range (LR) Heisenberg model in two dimensions (2D) up to linear size $L=8192$. We show that the system enters a long-range-ordered phase through a single continuous phase transition for all $\\sigma \\leq 2$, including the marginal case $\\sigma=2$. In contrast, for $\\sigma > 2$ it recovers the SR asymptotically free behavior with no finite-t","authors_text":"Dingyun Yao, Lode Polle, Tianning Xiao, Youjin Deng, Zhijie Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-12-01T18:06:48Z","title":"Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01956","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":"sha256:41cd9dee52920fdc2aa180ae891f178fe1f0548d6eb8701e788666f6c4ae2064","target":"record","created_at":"2026-06-04T01:08:36Z","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":"46096d6d8f7b5a90788584fa8ed9a77d662d2d87c31a05b560c982dd6db50ad4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-12-01T18:06:48Z","title_canon_sha256":"5eaf1ae384d1c8d688dfdb1d5088f24885fb6e15babaffeaf824baa0e619ec17"},"schema_version":"1.0","source":{"id":"2512.01956","kind":"arxiv","version":2}},"canonical_sha256":"881ced5f3331d24a6f9ab462f7d07a7a78880f93c1c782733a51696101535e36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"881ced5f3331d24a6f9ab462f7d07a7a78880f93c1c782733a51696101535e36","first_computed_at":"2026-06-04T01:08:36.986716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:08:36.986716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUAiYmShv5qMnlZPePQOaOnae9WXbBobY4gm+Hq06/F4LAj2sHfB0aA4n1oTt96g0Xt2Wwswid26ch18OlxGBg==","signature_status":"signed_v1","signed_at":"2026-06-04T01:08:36.987505Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.01956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41cd9dee52920fdc2aa180ae891f178fe1f0548d6eb8701e788666f6c4ae2064","sha256:3630f173ae55282fc22d5716d8922eeeaf89106209af0fbef4067003c803fc27"],"state_sha256":"6d46aab3aaf159980aee723ccb5ab3afa48764595057ef2d17cabc51cad66080"}