{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:G4ZQ4DBAFCFUKCI7GPX4FWLLQS","short_pith_number":"pith:G4ZQ4DBA","canonical_record":{"source":{"id":"1109.3377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2011-09-15T15:11:38Z","cross_cats_sorted":[],"title_canon_sha256":"b88ff66b95270f4126511af17698bd6efbea82c60cc1fd3501335b669e3b2d73","abstract_canon_sha256":"a9109af2d08894109c7843cdb9ad274a5fccb508b5075e5f6b5ada7b2abf8003"},"schema_version":"1.0"},"canonical_sha256":"37330e0c20288b45091f33efc2d96b84b9d3d3d112b23d4e432afac78d3e0a62","source":{"kind":"arxiv","id":"1109.3377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3377","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3377v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3377","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"G4ZQ4DBAFCFU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4ZQ4DBAFCFUKCI7","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4ZQ4DBA","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:G4ZQ4DBAFCFUKCI7GPX4FWLLQS","target":"record","payload":{"canonical_record":{"source":{"id":"1109.3377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2011-09-15T15:11:38Z","cross_cats_sorted":[],"title_canon_sha256":"b88ff66b95270f4126511af17698bd6efbea82c60cc1fd3501335b669e3b2d73","abstract_canon_sha256":"a9109af2d08894109c7843cdb9ad274a5fccb508b5075e5f6b5ada7b2abf8003"},"schema_version":"1.0"},"canonical_sha256":"37330e0c20288b45091f33efc2d96b84b9d3d3d112b23d4e432afac78d3e0a62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:56.870832Z","signature_b64":"qwwaKIj78KDKXX8a7gIP92obBqYgc8jt97fLY6iq0sbtF3hmNYHxdnFcIOeyK/oX9Pm2rkcqYt/p+mMRb8xJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37330e0c20288b45091f33efc2d96b84b9d3d3d112b23d4e432afac78d3e0a62","last_reissued_at":"2026-05-18T04:12:56.870247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:56.870247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.3377","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kh68fp+VJCuqqxl7XiP3TfblksGn7voV9AEwxSwzDCoXVbGfauGDdAyURmL/2GFiNM3MpWueaRMbLgV8AIiBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:09:22.893011Z"},"content_sha256":"8e8d497bb8d4b84c9de2f220bc64b7f0c75c1d5f2410059be98d004a94b550f8","schema_version":"1.0","event_id":"sha256:8e8d497bb8d4b84c9de2f220bc64b7f0c75c1d5f2410059be98d004a94b550f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:G4ZQ4DBAFCFUKCI7GPX4FWLLQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Amplitude and phase mode in a Bose Einstein condensate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Aranya B. Bhattacherjee","submitted_at":"2011-09-15T15:11:38Z","abstract_excerpt":"We show that starting from the Heisenberg equations of motion for Bose annihilation and creation operators and using an appropriate transformation, we can split the Bogoliubov mode into a free particle mode and the amplitude mode. We show this for both the free Bose gas as well as the Bose gas in an optical lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3377","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9KEugVnKo9uyD0zviL5rdVaRVqi/ZsuB/Rx4epT1wnVJJ50aVNSN8DFzZFMGsoyYYIJ1HHE1fXPP1mLbMPrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:09:22.893365Z"},"content_sha256":"482d912b6e02cb7f00c941da6629cb45c04eb5ac501a681b7cd1e9b1766a8a13","schema_version":"1.0","event_id":"sha256:482d912b6e02cb7f00c941da6629cb45c04eb5ac501a681b7cd1e9b1766a8a13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/bundle.json","state_url":"https://pith.science/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/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":"2026-05-30T06:09:22Z","links":{"resolver":"https://pith.science/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS","bundle":"https://pith.science/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/bundle.json","state":"https://pith.science/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4ZQ4DBAFCFUKCI7GPX4FWLLQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G4ZQ4DBAFCFUKCI7GPX4FWLLQS","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":"a9109af2d08894109c7843cdb9ad274a5fccb508b5075e5f6b5ada7b2abf8003","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2011-09-15T15:11:38Z","title_canon_sha256":"b88ff66b95270f4126511af17698bd6efbea82c60cc1fd3501335b669e3b2d73"},"schema_version":"1.0","source":{"id":"1109.3377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3377","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3377v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3377","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"G4ZQ4DBAFCFU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4ZQ4DBAFCFUKCI7","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4ZQ4DBA","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:482d912b6e02cb7f00c941da6629cb45c04eb5ac501a681b7cd1e9b1766a8a13","target":"graph","created_at":"2026-05-18T04:12:56Z","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":"We show that starting from the Heisenberg equations of motion for Bose annihilation and creation operators and using an appropriate transformation, we can split the Bogoliubov mode into a free particle mode and the amplitude mode. We show this for both the free Bose gas as well as the Bose gas in an optical lattice.","authors_text":"Aranya B. Bhattacherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2011-09-15T15:11:38Z","title":"Amplitude and phase mode in a Bose Einstein condensate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3377","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":"sha256:8e8d497bb8d4b84c9de2f220bc64b7f0c75c1d5f2410059be98d004a94b550f8","target":"record","created_at":"2026-05-18T04:12:56Z","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":"a9109af2d08894109c7843cdb9ad274a5fccb508b5075e5f6b5ada7b2abf8003","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2011-09-15T15:11:38Z","title_canon_sha256":"b88ff66b95270f4126511af17698bd6efbea82c60cc1fd3501335b669e3b2d73"},"schema_version":"1.0","source":{"id":"1109.3377","kind":"arxiv","version":1}},"canonical_sha256":"37330e0c20288b45091f33efc2d96b84b9d3d3d112b23d4e432afac78d3e0a62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37330e0c20288b45091f33efc2d96b84b9d3d3d112b23d4e432afac78d3e0a62","first_computed_at":"2026-05-18T04:12:56.870247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.870247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwwaKIj78KDKXX8a7gIP92obBqYgc8jt97fLY6iq0sbtF3hmNYHxdnFcIOeyK/oX9Pm2rkcqYt/p+mMRb8xJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.870832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e8d497bb8d4b84c9de2f220bc64b7f0c75c1d5f2410059be98d004a94b550f8","sha256:482d912b6e02cb7f00c941da6629cb45c04eb5ac501a681b7cd1e9b1766a8a13"],"state_sha256":"b1170c5b869cfe440bd78dbcb53a4bc967dd4a9532ae8edc7c819e878cbd7665"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g7LMlhnqxNn7wN+u+cjpx/hjEeQQgkDWW5dDmmrwHwnxkCOduIPJKhBR3DFY/CnVTq5h37lWYIYBO7tcDP0AAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:09:22.895398Z","bundle_sha256":"0da1d2c4e23080e800d4e3326ae90eef2d3b11f3e64824e67fdafb85071a1335"}}