{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GBAENWC22YLP5357JTF6P6YSO7","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":"ac7445d0d098ec148c50d7dab30000e9eb6a6dc4243e36a3948ab3b49125c3bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-10-17T14:12:02Z","title_canon_sha256":"7cdd6948aa857a89bcdad4afb7e83b510fd64b3b951858eb665a620027316800"},"schema_version":"1.0","source":{"id":"2410.13576","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.13576","created_at":"2026-07-05T11:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"2410.13576v3","created_at":"2026-07-05T11:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.13576","created_at":"2026-07-05T11:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"GBAENWC22YLP","created_at":"2026-07-05T11:39:05Z"},{"alias_kind":"pith_short_16","alias_value":"GBAENWC22YLP5357","created_at":"2026-07-05T11:39:05Z"},{"alias_kind":"pith_short_8","alias_value":"GBAENWC2","created_at":"2026-07-05T11:39:05Z"}],"graph_snapshots":[{"event_id":"sha256:54af5ecaf3f0ad2101c2e8a4e82be3a3aa7b9e880865726c651bc09a42bb236e","target":"graph","created_at":"2026-07-05T11:39:05Z","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/2410.13576/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a Bose gas on the unit torus at zero temperature in the Gross-Pitaevskii regime, known to perform Bose-Einstein condensation: a macroscopic fraction of the bosons occupy the same quantum state, called condensate. We study the Bose gas' quantum depletion, that is the number of bosons outside the condensate, and derive an explicit asymptotic formula of its generating function. Moreover, we prove an upper bound for the tails of the quantum depletion.","authors_text":"Simone Rademacher","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-10-17T14:12:02Z","title":"Generating function for quantum depletion of Bose-Einstein condensates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13576","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":"sha256:9b1526e56da869cc32f4206b163c4e77bd94f4b9b9b579b60b499693ec33e940","target":"record","created_at":"2026-07-05T11:39:05Z","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":"ac7445d0d098ec148c50d7dab30000e9eb6a6dc4243e36a3948ab3b49125c3bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-10-17T14:12:02Z","title_canon_sha256":"7cdd6948aa857a89bcdad4afb7e83b510fd64b3b951858eb665a620027316800"},"schema_version":"1.0","source":{"id":"2410.13576","kind":"arxiv","version":3}},"canonical_sha256":"304046d85ad616feefbf4ccbe7fb1277c0829526b354e396c52c4cda27c0bc32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"304046d85ad616feefbf4ccbe7fb1277c0829526b354e396c52c4cda27c0bc32","first_computed_at":"2026-07-05T11:39:05.019940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:05.019940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pVzA+lMCBpsUIsKeqXbK5mJ0hIqCbxdKCdVpPC5dt3xLTl6tMMomWhyPegT90bevOTOCjP+PhI8Qd8PVxUhCAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:05.020348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.13576","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b1526e56da869cc32f4206b163c4e77bd94f4b9b9b579b60b499693ec33e940","sha256:54af5ecaf3f0ad2101c2e8a4e82be3a3aa7b9e880865726c651bc09a42bb236e"],"state_sha256":"e1f84cf7113105039f2d58836d57f310ad2b15c57accdd2eee2f97e36451c5d3"}