{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HODEZJR4NLOHXWK43MWHA6T7W6","short_pith_number":"pith:HODEZJR4","canonical_record":{"source":{"id":"1607.08084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-07-27T13:25:39Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"50d3ac300fd69e3477470b9c0a1096c3206e41aabf29527a45d27595db6c495d","abstract_canon_sha256":"9c86e56e7feb98450a023cdb3ae0652d3d47aced66e3931a228ce653ddc29216"},"schema_version":"1.0"},"canonical_sha256":"3b864ca63c6adc7bd95cdb2c707a7fb7bf091748969e483ac4164638b0c87288","source":{"kind":"arxiv","id":"1607.08084","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08084","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08084v1","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08084","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"HODEZJR4NLOH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HODEZJR4NLOHXWK4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HODEZJR4","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HODEZJR4NLOHXWK43MWHA6T7W6","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-07-27T13:25:39Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"50d3ac300fd69e3477470b9c0a1096c3206e41aabf29527a45d27595db6c495d","abstract_canon_sha256":"9c86e56e7feb98450a023cdb3ae0652d3d47aced66e3931a228ce653ddc29216"},"schema_version":"1.0"},"canonical_sha256":"3b864ca63c6adc7bd95cdb2c707a7fb7bf091748969e483ac4164638b0c87288","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:47.613497Z","signature_b64":"kEO6SMCOQVfB1HonuchX4cg1iKiyqtYYc/fl87w9JHNMshhUDJ+BO7JxqekCfCxrLq3j7FAUMSJaPNZl9S8rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b864ca63c6adc7bd95cdb2c707a7fb7bf091748969e483ac4164638b0c87288","last_reissued_at":"2026-05-18T00:51:47.612871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:47.612871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08084","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":"2026-05-18T00:51:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTxBFmHNwOhtOQOauBa/CiuclBgpIawdPgrGwjU5XJbFyb838bY9X6zs/5q6fzt4cnWK8d7c6Jcp0/JEeUjICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:02:28.311976Z"},"content_sha256":"93861c1c71645eb31895e9af8c096fc0a30839811cf4b89662a127316bce9467","schema_version":"1.0","event_id":"sha256:93861c1c71645eb31895e9af8c096fc0a30839811cf4b89662a127316bce9467"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HODEZJR4NLOHXWK43MWHA6T7W6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lindblad Equation for the Inelastic Loss of Ultracold Atoms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Eric Braaten, G. Peter Lepage, H.-W. Hammer","submitted_at":"2016-07-27T13:25:39Z","abstract_excerpt":"The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08084","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":""},"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":"2026-05-18T00:51:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5gUjhj5bUrhyusYcblIqOyLU7fZ06GSyC2L0Bmr2wfmB9Qdwg5FdbKHCGiDZPHMHyMN3DlVtAayQFr4/9sbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:02:28.312652Z"},"content_sha256":"08f88f00e363a77ef98616a5be42372849d03afd3aae09d07137ec03d7583913","schema_version":"1.0","event_id":"sha256:08f88f00e363a77ef98616a5be42372849d03afd3aae09d07137ec03d7583913"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HODEZJR4NLOHXWK43MWHA6T7W6/bundle.json","state_url":"https://pith.science/pith/HODEZJR4NLOHXWK43MWHA6T7W6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HODEZJR4NLOHXWK43MWHA6T7W6/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":"2026-05-26T20:02:28Z","links":{"resolver":"https://pith.science/pith/HODEZJR4NLOHXWK43MWHA6T7W6","bundle":"https://pith.science/pith/HODEZJR4NLOHXWK43MWHA6T7W6/bundle.json","state":"https://pith.science/pith/HODEZJR4NLOHXWK43MWHA6T7W6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HODEZJR4NLOHXWK43MWHA6T7W6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HODEZJR4NLOHXWK43MWHA6T7W6","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":"9c86e56e7feb98450a023cdb3ae0652d3d47aced66e3931a228ce653ddc29216","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-07-27T13:25:39Z","title_canon_sha256":"50d3ac300fd69e3477470b9c0a1096c3206e41aabf29527a45d27595db6c495d"},"schema_version":"1.0","source":{"id":"1607.08084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08084","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08084v1","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08084","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"HODEZJR4NLOH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HODEZJR4NLOHXWK4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HODEZJR4","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:08f88f00e363a77ef98616a5be42372849d03afd3aae09d07137ec03d7583913","target":"graph","created_at":"2026-05-18T00:51:47Z","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"},"paper":{"abstract_excerpt":"The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the l","authors_text":"Eric Braaten, G. Peter Lepage, H.-W. Hammer","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-07-27T13:25:39Z","title":"Lindblad Equation for the Inelastic Loss of Ultracold Atoms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08084","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":"sha256:93861c1c71645eb31895e9af8c096fc0a30839811cf4b89662a127316bce9467","target":"record","created_at":"2026-05-18T00:51:47Z","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":"9c86e56e7feb98450a023cdb3ae0652d3d47aced66e3931a228ce653ddc29216","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-07-27T13:25:39Z","title_canon_sha256":"50d3ac300fd69e3477470b9c0a1096c3206e41aabf29527a45d27595db6c495d"},"schema_version":"1.0","source":{"id":"1607.08084","kind":"arxiv","version":1}},"canonical_sha256":"3b864ca63c6adc7bd95cdb2c707a7fb7bf091748969e483ac4164638b0c87288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b864ca63c6adc7bd95cdb2c707a7fb7bf091748969e483ac4164638b0c87288","first_computed_at":"2026-05-18T00:51:47.612871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:47.612871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kEO6SMCOQVfB1HonuchX4cg1iKiyqtYYc/fl87w9JHNMshhUDJ+BO7JxqekCfCxrLq3j7FAUMSJaPNZl9S8rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:47.613497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93861c1c71645eb31895e9af8c096fc0a30839811cf4b89662a127316bce9467","sha256:08f88f00e363a77ef98616a5be42372849d03afd3aae09d07137ec03d7583913"],"state_sha256":"dad976b1616700d4446bcc63265fbabce0bc2e4f293886cf2737da4a09c8f54c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaLm2mN/iHJoQ+VXI38ImIgaaWG4uUQmdIEPKGfDdvBV5sVD1yfrmZ1r71m0eZH4D6DVBJBB/496PNZbjUk4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:02:28.316472Z","bundle_sha256":"3dbfa43f1fc41a12e03a18e90005b675d1ba98936b3b42516b088befb7d0f5ad"}}