{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6GTJP3OOTKIQTM5AYJKP3RMS7R","short_pith_number":"pith:6GTJP3OO","canonical_record":{"source":{"id":"2407.10650","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-15T12:12:22Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"912beca268adc64dd90c74e86519238e2339e055575e5a54022a4083d47fd587","abstract_canon_sha256":"6ac2b479f2c8fd89f90d6f67fbdf87c2f73ab9cc292c3c748bc1cd9e4bf34d2a"},"schema_version":"1.0"},"canonical_sha256":"f1a697edce9a9109b3a0c254fdc592fc62d8c439b3bd71002814dee0be59b0b3","source":{"kind":"arxiv","id":"2407.10650","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.10650","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"2407.10650v1","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10650","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"6GTJP3OOTKIQ","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_16","alias_value":"6GTJP3OOTKIQTM5A","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_8","alias_value":"6GTJP3OO","created_at":"2026-07-05T11:33:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6GTJP3OOTKIQTM5AYJKP3RMS7R","target":"record","payload":{"canonical_record":{"source":{"id":"2407.10650","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-15T12:12:22Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"912beca268adc64dd90c74e86519238e2339e055575e5a54022a4083d47fd587","abstract_canon_sha256":"6ac2b479f2c8fd89f90d6f67fbdf87c2f73ab9cc292c3c748bc1cd9e4bf34d2a"},"schema_version":"1.0"},"canonical_sha256":"f1a697edce9a9109b3a0c254fdc592fc62d8c439b3bd71002814dee0be59b0b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:47.717741Z","signature_b64":"jUFo1kNd2u3tBvXaMFis5tlXx1DUI7moDyh4gZQajyFiqch2ZkdvLq+KEZhuZcip+JZ+y/rjng3h8xBd7vjNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1a697edce9a9109b3a0c254fdc592fc62d8c439b3bd71002814dee0be59b0b3","last_reissued_at":"2026-07-05T11:33:47.717274Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:47.717274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.10650","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A12mRgankAMOpqNkSEtedQ0Xoj2mpOxaWOLFizPINdE+5ZyevDc9zJBUCaTGC65U7xr575jfFWs5WR5Fa7sVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:35:15.390705Z"},"content_sha256":"96f475ea57ff9a9b45e919ce2034918befad86ec22adfb278180844a6908f58b","schema_version":"1.0","event_id":"sha256:96f475ea57ff9a9b45e919ce2034918befad86ec22adfb278180844a6908f58b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6GTJP3OOTKIQTM5AYJKP3RMS7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Christian Brennecke, Wilhelm Kroschinsky","submitted_at":"2024-07-15T12:12:22Z","abstract_excerpt":"We revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is described by the time-dependent Gross-Pitaevskii equation. Like the recent work \\cite{BS}, we obtain optimal bounds on the number of excitations orthogonal to the condensate state. In contrast to \\cite{BS}, however, whose main strategy consists of controlling the number of excitations with regards to a suitable fluctuation dynamics $t\\mapsto e^{-B_t} e^{-iH_Nt}$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10650","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.10650/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8PhbNmd5bcOuxAX+Nlwfpp57PAq6m0QKMoqhCqUC4JT4TvQhtUvZmw5yugMmTE+zUR1hbnVNp5Zkv4xQhuiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:35:15.391309Z"},"content_sha256":"17c77f7d279a67b771df4df36faa5d4df8d724d50f58fddc4f43783fde14a208","schema_version":"1.0","event_id":"sha256:17c77f7d279a67b771df4df36faa5d4df8d724d50f58fddc4f43783fde14a208"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/bundle.json","state_url":"https://pith.science/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T11:35:15Z","links":{"resolver":"https://pith.science/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R","bundle":"https://pith.science/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/bundle.json","state":"https://pith.science/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GTJP3OOTKIQTM5AYJKP3RMS7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6GTJP3OOTKIQTM5AYJKP3RMS7R","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":"6ac2b479f2c8fd89f90d6f67fbdf87c2f73ab9cc292c3c748bc1cd9e4bf34d2a","cross_cats_sorted":["math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-15T12:12:22Z","title_canon_sha256":"912beca268adc64dd90c74e86519238e2339e055575e5a54022a4083d47fd587"},"schema_version":"1.0","source":{"id":"2407.10650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.10650","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"2407.10650v1","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10650","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"6GTJP3OOTKIQ","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_16","alias_value":"6GTJP3OOTKIQTM5A","created_at":"2026-07-05T11:33:47Z"},{"alias_kind":"pith_short_8","alias_value":"6GTJP3OO","created_at":"2026-07-05T11:33:47Z"}],"graph_snapshots":[{"event_id":"sha256:17c77f7d279a67b771df4df36faa5d4df8d724d50f58fddc4f43783fde14a208","target":"graph","created_at":"2026-07-05T11:33:47Z","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/2407.10650/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is described by the time-dependent Gross-Pitaevskii equation. Like the recent work \\cite{BS}, we obtain optimal bounds on the number of excitations orthogonal to the condensate state. In contrast to \\cite{BS}, however, whose main strategy consists of controlling the number of excitations with regards to a suitable fluctuation dynamics $t\\mapsto e^{-B_t} e^{-iH_Nt}$ wi","authors_text":"Christian Brennecke, Wilhelm Kroschinsky","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-15T12:12:22Z","title":"Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10650","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":"sha256:96f475ea57ff9a9b45e919ce2034918befad86ec22adfb278180844a6908f58b","target":"record","created_at":"2026-07-05T11:33:47Z","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":"6ac2b479f2c8fd89f90d6f67fbdf87c2f73ab9cc292c3c748bc1cd9e4bf34d2a","cross_cats_sorted":["math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-15T12:12:22Z","title_canon_sha256":"912beca268adc64dd90c74e86519238e2339e055575e5a54022a4083d47fd587"},"schema_version":"1.0","source":{"id":"2407.10650","kind":"arxiv","version":1}},"canonical_sha256":"f1a697edce9a9109b3a0c254fdc592fc62d8c439b3bd71002814dee0be59b0b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1a697edce9a9109b3a0c254fdc592fc62d8c439b3bd71002814dee0be59b0b3","first_computed_at":"2026-07-05T11:33:47.717274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:47.717274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jUFo1kNd2u3tBvXaMFis5tlXx1DUI7moDyh4gZQajyFiqch2ZkdvLq+KEZhuZcip+JZ+y/rjng3h8xBd7vjNBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:47.717741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.10650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f475ea57ff9a9b45e919ce2034918befad86ec22adfb278180844a6908f58b","sha256:17c77f7d279a67b771df4df36faa5d4df8d724d50f58fddc4f43783fde14a208"],"state_sha256":"8accc8631346a0058efd7009257f19cd77def5c9a251bb18b54c0347b31e5477"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NNWumSmC+9zOAZNe389MJAC0fWfOZDCXfoohGgqAKLwYd0TFnWYCwxMQJhqjqbmR0gckR3gLdQqVzDM1mDZyDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:35:15.395198Z","bundle_sha256":"14efcd8496053cf7bcd5495d1ad1e74022be37b2a38b3d6274aaea2ceee851c0"}}