{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AP2KGELQLIPRVUYVRYZ3IQEWPR","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":"ae0a87231bb6e9e1a930c33533bef37b81f6573c3f61c1fa7496ac562b31bb3a","cross_cats_sorted":["math.AP","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-31T18:58:28Z","title_canon_sha256":"980861bb3d67836bd04232692814fef642d6cfd3397c239bd45bee28fedc5ea9"},"schema_version":"1.0","source":{"id":"2501.19402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.19402","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"2501.19402v3","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.19402","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"AP2KGELQLIPR","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_16","alias_value":"AP2KGELQLIPRVUYV","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_8","alias_value":"AP2KGELQ","created_at":"2026-07-05T11:44:00Z"}],"graph_snapshots":[{"event_id":"sha256:aee016fee90ef9e6157fbfcf1a5157ebf8dda265b4a4cf0b642cba78763ac2bd","target":"graph","created_at":"2026-07-05T11:44:00Z","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/2501.19402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds to the temperature scale of the Bose--Einstein condensation phase transition. We show that spontaneous $U(1)$ symmetry breaking occurs if and only if the system exhibits Bose--Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.","authors_text":"Andreas Deuchert, Marcin Napiorkowski, Phan Thanh Nam","cross_cats":["math.AP","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-31T18:58:28Z","title":"A note on spontaneous symmetry breaking in the mean-field Bose gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19402","kind":"arxiv","version":3},"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:b590a4e090f3a4a7d3dd4c43225c96034c32e2088585c7e04ebf98ffe14bf873","target":"record","created_at":"2026-07-05T11:44:00Z","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":"ae0a87231bb6e9e1a930c33533bef37b81f6573c3f61c1fa7496ac562b31bb3a","cross_cats_sorted":["math.AP","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-31T18:58:28Z","title_canon_sha256":"980861bb3d67836bd04232692814fef642d6cfd3397c239bd45bee28fedc5ea9"},"schema_version":"1.0","source":{"id":"2501.19402","kind":"arxiv","version":3}},"canonical_sha256":"03f4a311705a1f1ad3158e33b440967c6b86f0f5051bf7f385da2acf330cce1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03f4a311705a1f1ad3158e33b440967c6b86f0f5051bf7f385da2acf330cce1c","first_computed_at":"2026-07-05T11:44:00.672898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:00.672898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bx4IcI8hS1SGRQlrpHzG7dlmzvDf08ITgtBy0bFL1adGUFROYERsg15EsU2dk7H4kkXtDTcSdEgffwa4H9usAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:00.673398Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.19402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b590a4e090f3a4a7d3dd4c43225c96034c32e2088585c7e04ebf98ffe14bf873","sha256:aee016fee90ef9e6157fbfcf1a5157ebf8dda265b4a4cf0b642cba78763ac2bd"],"state_sha256":"2d1c54132b78778274403737bee1420f257cc0125ee7611dfb222df66e88f895"}