{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:ZB33UIOBIC6JACQJ6J3KZJFYNG","short_pith_number":"pith:ZB33UIOB","canonical_record":{"source":{"id":"cond-mat/9703199","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-03-24T08:05:39Z","cross_cats_sorted":[],"title_canon_sha256":"349b0a76f7b3bd7eaa86848c0cc14a9e8d1fbe5828fd15de4e91081c16feedf3","abstract_canon_sha256":"9e5cc191fc9eee6a04b8f401cd65038e88019e323d3aef630c849a9bcb6c2e94"},"schema_version":"1.0"},"canonical_sha256":"c877ba21c140bc900a09f276aca4b869a9451e16ae47ced053e08be10af5be22","source":{"kind":"arxiv","id":"cond-mat/9703199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9703199","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9703199v2","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9703199","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZB33UIOBIC6J","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZB33UIOBIC6JACQJ","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZB33UIOB","created_at":"2026-07-04T16:03:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:ZB33UIOBIC6JACQJ6J3KZJFYNG","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9703199","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-03-24T08:05:39Z","cross_cats_sorted":[],"title_canon_sha256":"349b0a76f7b3bd7eaa86848c0cc14a9e8d1fbe5828fd15de4e91081c16feedf3","abstract_canon_sha256":"9e5cc191fc9eee6a04b8f401cd65038e88019e323d3aef630c849a9bcb6c2e94"},"schema_version":"1.0"},"canonical_sha256":"c877ba21c140bc900a09f276aca4b869a9451e16ae47ced053e08be10af5be22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:03:46.037827Z","signature_b64":"LYedUjs7DPgM8EleJsm8vgdy4Npv6Ega8LPSCdVpnxWjU7BhXpElxYAGvY/kd7cLInoKw+WrrUacEmYcUleSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c877ba21c140bc900a09f276aca4b869a9451e16ae47ced053e08be10af5be22","last_reissued_at":"2026-07-04T16:03:46.037391Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:03:46.037391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9703199","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WAH9O0q153Ov2sKKoqf0uSvfoRJlDOSBAmiKfd4t8l1LiaBYfmluzfoc+DTdoNFVTbKX89reNS3auO++/+aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:09:25.642421Z"},"content_sha256":"15217664de544fdc6f3e3d231a1c13b85a01cb5b60831d785f69ad7a77846226","schema_version":"1.0","event_id":"sha256:15217664de544fdc6f3e3d231a1c13b85a01cb5b60831d785f69ad7a77846226"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:ZB33UIOBIC6JACQJ6J3KZJFYNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"H.T.C. Stoof, K. Burnett, N.P. Proukakis","submitted_at":"1997-03-24T08:05:39Z","abstract_excerpt":"In this paper we use microscopic arguments to derive a nonlinear Schr\\\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9703199","kind":"arxiv","version":2},"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/cond-mat/9703199/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":"2026-07-04T16:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aiSDEBvDzF0kQUCPG+JYniNkSQ00nWqsmybGcfjDNvc47dnwo18B35znqnL4f5BYcLeuZ90ymYQ2vi3YZw9WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:09:25.642818Z"},"content_sha256":"ae6c80d5ed4441de793ab9d166f854874b98c2545fc694fc21ab3a615f6d50c8","schema_version":"1.0","event_id":"sha256:ae6c80d5ed4441de793ab9d166f854874b98c2545fc694fc21ab3a615f6d50c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/bundle.json","state_url":"https://pith.science/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/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":"2026-08-03T17:09:25Z","links":{"resolver":"https://pith.science/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG","bundle":"https://pith.science/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/bundle.json","state":"https://pith.science/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZB33UIOBIC6JACQJ6J3KZJFYNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:ZB33UIOBIC6JACQJ6J3KZJFYNG","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":"9e5cc191fc9eee6a04b8f401cd65038e88019e323d3aef630c849a9bcb6c2e94","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-03-24T08:05:39Z","title_canon_sha256":"349b0a76f7b3bd7eaa86848c0cc14a9e8d1fbe5828fd15de4e91081c16feedf3"},"schema_version":"1.0","source":{"id":"cond-mat/9703199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9703199","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9703199v2","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9703199","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZB33UIOBIC6J","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZB33UIOBIC6JACQJ","created_at":"2026-07-04T16:03:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZB33UIOB","created_at":"2026-07-04T16:03:46Z"}],"graph_snapshots":[{"event_id":"sha256:ae6c80d5ed4441de793ab9d166f854874b98c2545fc694fc21ab3a615f6d50c8","target":"graph","created_at":"2026-07-04T16:03:46Z","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/cond-mat/9703199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we use microscopic arguments to derive a nonlinear Schr\\\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how ","authors_text":"H.T.C. Stoof, K. Burnett, N.P. Proukakis","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-03-24T08:05:39Z","title":"Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9703199","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":"sha256:15217664de544fdc6f3e3d231a1c13b85a01cb5b60831d785f69ad7a77846226","target":"record","created_at":"2026-07-04T16:03:46Z","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":"9e5cc191fc9eee6a04b8f401cd65038e88019e323d3aef630c849a9bcb6c2e94","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-03-24T08:05:39Z","title_canon_sha256":"349b0a76f7b3bd7eaa86848c0cc14a9e8d1fbe5828fd15de4e91081c16feedf3"},"schema_version":"1.0","source":{"id":"cond-mat/9703199","kind":"arxiv","version":2}},"canonical_sha256":"c877ba21c140bc900a09f276aca4b869a9451e16ae47ced053e08be10af5be22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c877ba21c140bc900a09f276aca4b869a9451e16ae47ced053e08be10af5be22","first_computed_at":"2026-07-04T16:03:46.037391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:03:46.037391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LYedUjs7DPgM8EleJsm8vgdy4Npv6Ega8LPSCdVpnxWjU7BhXpElxYAGvY/kd7cLInoKw+WrrUacEmYcUleSBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:03:46.037827Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9703199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15217664de544fdc6f3e3d231a1c13b85a01cb5b60831d785f69ad7a77846226","sha256:ae6c80d5ed4441de793ab9d166f854874b98c2545fc694fc21ab3a615f6d50c8"],"state_sha256":"3b75fdd54e8026e563f9f9859811ee6820f7e4240ae712a7b645300263100ecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeCs7UxI5LrCmKRSHMe5ECrxOeztTPd9ICLzs0WMao3SuDHNLsiWGDGqBJIPwk7gJRKsw8KOZNNOYDLBRjvMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:09:25.645447Z","bundle_sha256":"68f050cde764ecde16aaec6255067d24540bbad3a7ebc384f104f530ec44fc8f"}}