{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2UED6J3WYYJOJRNRYDNT363OO2","short_pith_number":"pith:2UED6J3W","canonical_record":{"source":{"id":"1209.5446","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-24T22:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"f5269b813127bbfb6e2bae9e4f58067ab74329072f23dda8deecd2da0cb98558","abstract_canon_sha256":"291f5585a773ce88ed6817f0f9196fb54e3a55bef342c8b5faea7fcfe620e031"},"schema_version":"1.0"},"canonical_sha256":"d5083f2776c612e4c5b1c0db3dfb6e768ada75c774895065cffbfa36b78ea2a6","source":{"kind":"arxiv","id":"1209.5446","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5446","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5446v2","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5446","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"2UED6J3WYYJO","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2UED6J3WYYJOJRNR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2UED6J3W","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2UED6J3WYYJOJRNRYDNT363OO2","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5446","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-24T22:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"f5269b813127bbfb6e2bae9e4f58067ab74329072f23dda8deecd2da0cb98558","abstract_canon_sha256":"291f5585a773ce88ed6817f0f9196fb54e3a55bef342c8b5faea7fcfe620e031"},"schema_version":"1.0"},"canonical_sha256":"d5083f2776c612e4c5b1c0db3dfb6e768ada75c774895065cffbfa36b78ea2a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:55.297229Z","signature_b64":"G6hMPv2k0iojONIOwKN9l6S4V2O3H3Maq0K7PWVNDpz2FEyxh5LY+B4irVm1ekEDHDaAUVBa2G3wB3JkMKM7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5083f2776c612e4c5b1c0db3dfb6e768ada75c774895065cffbfa36b78ea2a6","last_reissued_at":"2026-05-18T03:30:55.296387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:55.296387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5446","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":"2026-05-18T03:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OVTC7fH76A6nJyLUAnLn/a7KADw3xFwTRG3m06ilGn7+0lF8AL/GUcE4CPBSf7v5hYleKvdn+HkvYFuydiQcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:23.903997Z"},"content_sha256":"dda842d1fa91577e0307c51d6ab7d6dae7c235af95f12af442264a97479301d5","schema_version":"1.0","event_id":"sha256:dda842d1fa91577e0307c51d6ab7d6dae7c235af95f12af442264a97479301d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2UED6J3WYYJOJRNRYDNT363OO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bogoliubov theory on the disordered lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Christopher Gaul, Cord A. M\\\"uller","submitted_at":"2012-09-24T22:18:18Z","abstract_excerpt":"Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5446","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":""},"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":"2026-05-18T03:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAX4HbQMTxfdaUpAWI2G2iJshySlv7D9y0S9ugICzjwkK/y3zw233DXSx3XgdoxWfy30VBsrgIIOomxvhAH0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:23.904686Z"},"content_sha256":"9fd2917787c0f10e43b8ff9eccbdb410d636a6a52d1e63e6d2c82e68ba138f0b","schema_version":"1.0","event_id":"sha256:9fd2917787c0f10e43b8ff9eccbdb410d636a6a52d1e63e6d2c82e68ba138f0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UED6J3WYYJOJRNRYDNT363OO2/bundle.json","state_url":"https://pith.science/pith/2UED6J3WYYJOJRNRYDNT363OO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UED6J3WYYJOJRNRYDNT363OO2/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":"2026-05-27T10:26:23Z","links":{"resolver":"https://pith.science/pith/2UED6J3WYYJOJRNRYDNT363OO2","bundle":"https://pith.science/pith/2UED6J3WYYJOJRNRYDNT363OO2/bundle.json","state":"https://pith.science/pith/2UED6J3WYYJOJRNRYDNT363OO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UED6J3WYYJOJRNRYDNT363OO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2UED6J3WYYJOJRNRYDNT363OO2","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":"291f5585a773ce88ed6817f0f9196fb54e3a55bef342c8b5faea7fcfe620e031","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-24T22:18:18Z","title_canon_sha256":"f5269b813127bbfb6e2bae9e4f58067ab74329072f23dda8deecd2da0cb98558"},"schema_version":"1.0","source":{"id":"1209.5446","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5446","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5446v2","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5446","created_at":"2026-05-18T03:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"2UED6J3WYYJO","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2UED6J3WYYJOJRNR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2UED6J3W","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9fd2917787c0f10e43b8ff9eccbdb410d636a6a52d1e63e6d2c82e68ba138f0b","target":"graph","created_at":"2026-05-18T03:30:55Z","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":"Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data.","authors_text":"Christopher Gaul, Cord A. M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-24T22:18:18Z","title":"Bogoliubov theory on the disordered lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5446","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:dda842d1fa91577e0307c51d6ab7d6dae7c235af95f12af442264a97479301d5","target":"record","created_at":"2026-05-18T03:30:55Z","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":"291f5585a773ce88ed6817f0f9196fb54e3a55bef342c8b5faea7fcfe620e031","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-24T22:18:18Z","title_canon_sha256":"f5269b813127bbfb6e2bae9e4f58067ab74329072f23dda8deecd2da0cb98558"},"schema_version":"1.0","source":{"id":"1209.5446","kind":"arxiv","version":2}},"canonical_sha256":"d5083f2776c612e4c5b1c0db3dfb6e768ada75c774895065cffbfa36b78ea2a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5083f2776c612e4c5b1c0db3dfb6e768ada75c774895065cffbfa36b78ea2a6","first_computed_at":"2026-05-18T03:30:55.296387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:55.296387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G6hMPv2k0iojONIOwKN9l6S4V2O3H3Maq0K7PWVNDpz2FEyxh5LY+B4irVm1ekEDHDaAUVBa2G3wB3JkMKM7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:55.297229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5446","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dda842d1fa91577e0307c51d6ab7d6dae7c235af95f12af442264a97479301d5","sha256:9fd2917787c0f10e43b8ff9eccbdb410d636a6a52d1e63e6d2c82e68ba138f0b"],"state_sha256":"3cecd723c5cee180f73f68e7fb2b9ad54568b528343f5855af7549ef56cffa23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tm0TOrhmusi804e4vj9+vL3flw876N+A0cgQmze2xVw6kqRYKSqc/jYUSN/Or2xTC3in0D2/rW5y6eyS3g4CCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:26:23.907713Z","bundle_sha256":"d0ab9fc5e9befbdc3c775a1f2878fbe49a9156058ee3cee349f613f65df08eaa"}}