{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:347RCSRZ2SB32JVY2TKGQ55JWG","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":"b7e1f9223692d9bc992162b4347e561f19f2f68a8393688f0de8ff5ee6ee5617","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-01-27T06:19:51Z","title_canon_sha256":"8d19ba504fdeacd97d6c4e814370e486469de81db3db1794653156bb6de4c290"},"schema_version":"1.0","source":{"id":"2501.15803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15803","created_at":"2026-07-05T10:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15803v1","created_at":"2026-07-05T10:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15803","created_at":"2026-07-05T10:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"347RCSRZ2SB3","created_at":"2026-07-05T10:05:50Z"},{"alias_kind":"pith_short_16","alias_value":"347RCSRZ2SB32JVY","created_at":"2026-07-05T10:05:50Z"},{"alias_kind":"pith_short_8","alias_value":"347RCSRZ","created_at":"2026-07-05T10:05:50Z"}],"graph_snapshots":[{"event_id":"sha256:ad13c3c740d7e975fa3f64195b7081092a8c3c9f85689c322c07d66ba5a810d7","target":"graph","created_at":"2026-07-05T10:05:50Z","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/2501.15803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider trapped Bose gases in three dimensions in the Gross-Pitaevskii regime whose low energy states are well known to exhibit Bose-Einstein condensation. That is, the majority of the particles occupies the same condensate state. We prove exponential control of the number of particles orthogonal to the condensate state, generalizing recent results for translation invariant systems.","authors_text":"Christian Brennecke, Nils Behrmann, Simone Rademacher","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-01-27T06:19:51Z","title":"Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15803","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":"sha256:76b93d8ed0054e2acc1e0168a6aa1ec8498e28c44bb6c6c7a4e7fb126ca43397","target":"record","created_at":"2026-07-05T10:05:50Z","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":"b7e1f9223692d9bc992162b4347e561f19f2f68a8393688f0de8ff5ee6ee5617","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-01-27T06:19:51Z","title_canon_sha256":"8d19ba504fdeacd97d6c4e814370e486469de81db3db1794653156bb6de4c290"},"schema_version":"1.0","source":{"id":"2501.15803","kind":"arxiv","version":1}},"canonical_sha256":"df3f114a39d483bd26b8d4d46877a9b1a8cb4968d685eaa9079a367704075c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df3f114a39d483bd26b8d4d46877a9b1a8cb4968d685eaa9079a367704075c2f","first_computed_at":"2026-07-05T10:05:50.833196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:50.833196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifRhW/2YmBnJZ7ivlXUM1Uj2UUPn6guXXC5nN0+er5UmwQx7nutFRHIeYLgzfiP2CAwsRKFhZmrwBmp/CSS/CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:50.833620Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76b93d8ed0054e2acc1e0168a6aa1ec8498e28c44bb6c6c7a4e7fb126ca43397","sha256:ad13c3c740d7e975fa3f64195b7081092a8c3c9f85689c322c07d66ba5a810d7"],"state_sha256":"1ed2484f3d8fc8267c14458c3bccf6944f6678cdde8ab3c73c623e6de2040d5e"}