{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QQXLAEGTY5G4MV5WIE5FSU3BJW","short_pith_number":"pith:QQXLAEGT","canonical_record":{"source":{"id":"1605.07815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-05-25T10:29:39Z","cross_cats_sorted":[],"title_canon_sha256":"5a677ee4f035d34aa21db562ea09c97f7ff95afb37a330189eba9337ac99e37b","abstract_canon_sha256":"f5d4aba61856851554d6dff46751bdf74446b8271b521f859e95d6a1489e5516"},"schema_version":"1.0"},"canonical_sha256":"842eb010d3c74dc657b6413a5953614db1dd5a30f4060725eb5f5659ccd2f7f9","source":{"kind":"arxiv","id":"1605.07815","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07815","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07815v1","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07815","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"QQXLAEGTY5G4","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QQXLAEGTY5G4MV5W","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QQXLAEGT","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QQXLAEGTY5G4MV5WIE5FSU3BJW","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-05-25T10:29:39Z","cross_cats_sorted":[],"title_canon_sha256":"5a677ee4f035d34aa21db562ea09c97f7ff95afb37a330189eba9337ac99e37b","abstract_canon_sha256":"f5d4aba61856851554d6dff46751bdf74446b8271b521f859e95d6a1489e5516"},"schema_version":"1.0"},"canonical_sha256":"842eb010d3c74dc657b6413a5953614db1dd5a30f4060725eb5f5659ccd2f7f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:11.475104Z","signature_b64":"OJ8lj+IHk7M9WEFwuNcxdEMAnCtrc0cNynQWDba0OunnriBV4YXUMFUSpEYKC+zX9U5m+Nnf56yFekgIFPdbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"842eb010d3c74dc657b6413a5953614db1dd5a30f4060725eb5f5659ccd2f7f9","last_reissued_at":"2026-05-18T01:12:11.474571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:11.474571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07815","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":"2026-05-18T01:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/E/B7X1UAv+jS14GOQ89yxCnwYN1UHeR23Ez04qc1z4i3rrK6dgX2DYReDAntd6NWh2G3zaLPcvNFMzXwpfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:40.966559Z"},"content_sha256":"4662de8ef92144c9833a5f43a225e098e3dde401d15e8fb0d0a7e4da04fc54c9","schema_version":"1.0","event_id":"sha256:4662de8ef92144c9833a5f43a225e098e3dde401d15e8fb0d0a7e4da04fc54c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QQXLAEGTY5G4MV5WIE5FSU3BJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theory of cold atoms: Bose-Einstein statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"V.I. Yukalov","submitted_at":"2016-05-25T10:29:39Z","abstract_excerpt":"This Tutorial is the continuation of the previous tutorial part, published in Laser Phys. 23, 062001 (2013), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded. In the present part, the specifics of the correct theoretical description of atoms obeying Bose-Einstein statistics are explained, including trapped Bose atoms. In the theory of systems exhibiting the phenomenon of Bose-Einstein condensation, there exists a number of delicate mathematical points, whose misunderstanding often results in principall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07815","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":"2026-05-18T01:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+L1+LkV/ahFvSsZ1YPr+9tKqwI2JNiPbtRRPySuiuNhtu2vFhksvugmpprTwu9NtIcxvnCBA4RK4hJyUGlpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:40.966906Z"},"content_sha256":"e881376ee14c7a8f1a28f3d0e71be5912adfec40eb18049816bf5652c1edd590","schema_version":"1.0","event_id":"sha256:e881376ee14c7a8f1a28f3d0e71be5912adfec40eb18049816bf5652c1edd590"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/bundle.json","state_url":"https://pith.science/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/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":"2026-06-02T02:48:40Z","links":{"resolver":"https://pith.science/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW","bundle":"https://pith.science/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/bundle.json","state":"https://pith.science/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQXLAEGTY5G4MV5WIE5FSU3BJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QQXLAEGTY5G4MV5WIE5FSU3BJW","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":"f5d4aba61856851554d6dff46751bdf74446b8271b521f859e95d6a1489e5516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-05-25T10:29:39Z","title_canon_sha256":"5a677ee4f035d34aa21db562ea09c97f7ff95afb37a330189eba9337ac99e37b"},"schema_version":"1.0","source":{"id":"1605.07815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07815","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07815v1","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07815","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"QQXLAEGTY5G4","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QQXLAEGTY5G4MV5W","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QQXLAEGT","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:e881376ee14c7a8f1a28f3d0e71be5912adfec40eb18049816bf5652c1edd590","target":"graph","created_at":"2026-05-18T01:12:11Z","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":"This Tutorial is the continuation of the previous tutorial part, published in Laser Phys. 23, 062001 (2013), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded. In the present part, the specifics of the correct theoretical description of atoms obeying Bose-Einstein statistics are explained, including trapped Bose atoms. In the theory of systems exhibiting the phenomenon of Bose-Einstein condensation, there exists a number of delicate mathematical points, whose misunderstanding often results in principall","authors_text":"V.I. Yukalov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-05-25T10:29:39Z","title":"Theory of cold atoms: Bose-Einstein statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07815","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":"sha256:4662de8ef92144c9833a5f43a225e098e3dde401d15e8fb0d0a7e4da04fc54c9","target":"record","created_at":"2026-05-18T01:12:11Z","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":"f5d4aba61856851554d6dff46751bdf74446b8271b521f859e95d6a1489e5516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-05-25T10:29:39Z","title_canon_sha256":"5a677ee4f035d34aa21db562ea09c97f7ff95afb37a330189eba9337ac99e37b"},"schema_version":"1.0","source":{"id":"1605.07815","kind":"arxiv","version":1}},"canonical_sha256":"842eb010d3c74dc657b6413a5953614db1dd5a30f4060725eb5f5659ccd2f7f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842eb010d3c74dc657b6413a5953614db1dd5a30f4060725eb5f5659ccd2f7f9","first_computed_at":"2026-05-18T01:12:11.474571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:11.474571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJ8lj+IHk7M9WEFwuNcxdEMAnCtrc0cNynQWDba0OunnriBV4YXUMFUSpEYKC+zX9U5m+Nnf56yFekgIFPdbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:11.475104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4662de8ef92144c9833a5f43a225e098e3dde401d15e8fb0d0a7e4da04fc54c9","sha256:e881376ee14c7a8f1a28f3d0e71be5912adfec40eb18049816bf5652c1edd590"],"state_sha256":"931b71415f3ee2b33a3e6f6cf24bb19af9ab9357262a1849bc0e077040dca7c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reI0+PxKOITIglxxlqNCj4cXmyNlOXPupX/BWIBNQ76yck9rF5qs2iAUXjh+v585b04WPayQaZl7EO7r/ksJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:48:40.968849Z","bundle_sha256":"7ba9ed88042c3ebfea7f1950acbebf46337e2758718a880d4d830ae92e7a326b"}}