{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6GB2MURYASOTNJP6PQMN5C7RHC","short_pith_number":"pith:6GB2MURY","canonical_record":{"source":{"id":"1304.6881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-25T11:34:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"111b670f49a03e5a656258221a1f49fb8c551e954b8ac57194c9edc90a927924","abstract_canon_sha256":"2a0f273ca19c02f5f5bdc15e80c05b0687a45b6c5bd57933c75b2b51c0557110"},"schema_version":"1.0"},"canonical_sha256":"f183a65238049d36a5fe7c18de8bf138abf1c88a4dd7eb9e677097b258ccfc67","source":{"kind":"arxiv","id":"1304.6881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6881","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6881v1","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6881","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"6GB2MURYASOT","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6GB2MURYASOTNJP6","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6GB2MURY","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6GB2MURYASOTNJP6PQMN5C7RHC","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-25T11:34:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"111b670f49a03e5a656258221a1f49fb8c551e954b8ac57194c9edc90a927924","abstract_canon_sha256":"2a0f273ca19c02f5f5bdc15e80c05b0687a45b6c5bd57933c75b2b51c0557110"},"schema_version":"1.0"},"canonical_sha256":"f183a65238049d36a5fe7c18de8bf138abf1c88a4dd7eb9e677097b258ccfc67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:21.972980Z","signature_b64":"S4x/xLzQiN2KSIA4EvGaNsz3tnylcV99xIzkCsA88tOOPawfBo2uBbddgBtVJLeQZ/5ssulbQiTojmVrCsHqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f183a65238049d36a5fe7c18de8bf138abf1c88a4dd7eb9e677097b258ccfc67","last_reissued_at":"2026-05-18T01:50:21.972207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:21.972207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6881","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":"2026-05-18T01:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7R2XyHjXtWECM4pH7Q3mLoz0k3812QxFPORpxDQt/uQgYKjPt3CUl2KhNgkud4p1muYiCFy/ufSCgutYWpmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:04:19.992741Z"},"content_sha256":"baa2dfe96eeb5a82009ee93cd92bd298e74abde75246ba7d76c873291fab160d","schema_version":"1.0","event_id":"sha256:baa2dfe96eeb5a82009ee93cd92bd298e74abde75246ba7d76c873291fab160d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6GB2MURYASOTNJP6PQMN5C7RHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theory of Cold Atoms: Basics of Quantum Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"V.I. Yukalov","submitted_at":"2013-04-25T11:34:02Z","abstract_excerpt":"The aim of this Tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term {\\it cold} implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. And the term {\\it atoms} means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are {\\it trapped} in the sense that they form a finite quantum system, though their number can be very large allowing for the use of the methods of statistical mechani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6881","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":"2026-05-18T01:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRoFvpohSP3Ag1jwLVcfFUmh5NB3fN31DairhzcGGaGie3lOZUAP5yqelfEIzVSGiH4pgJplJcxn8R49nb6ACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:04:19.993091Z"},"content_sha256":"4ed57a665cc06ddb5c3b261a7a4693be15cd43845519c247e8a9ba0889b28587","schema_version":"1.0","event_id":"sha256:4ed57a665cc06ddb5c3b261a7a4693be15cd43845519c247e8a9ba0889b28587"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GB2MURYASOTNJP6PQMN5C7RHC/bundle.json","state_url":"https://pith.science/pith/6GB2MURYASOTNJP6PQMN5C7RHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GB2MURYASOTNJP6PQMN5C7RHC/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":"2026-06-02T05:04:19Z","links":{"resolver":"https://pith.science/pith/6GB2MURYASOTNJP6PQMN5C7RHC","bundle":"https://pith.science/pith/6GB2MURYASOTNJP6PQMN5C7RHC/bundle.json","state":"https://pith.science/pith/6GB2MURYASOTNJP6PQMN5C7RHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GB2MURYASOTNJP6PQMN5C7RHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6GB2MURYASOTNJP6PQMN5C7RHC","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":"2a0f273ca19c02f5f5bdc15e80c05b0687a45b6c5bd57933c75b2b51c0557110","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-25T11:34:02Z","title_canon_sha256":"111b670f49a03e5a656258221a1f49fb8c551e954b8ac57194c9edc90a927924"},"schema_version":"1.0","source":{"id":"1304.6881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6881","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6881v1","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6881","created_at":"2026-05-18T01:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"6GB2MURYASOT","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6GB2MURYASOTNJP6","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6GB2MURY","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:4ed57a665cc06ddb5c3b261a7a4693be15cd43845519c247e8a9ba0889b28587","target":"graph","created_at":"2026-05-18T01:50:21Z","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 aim of this Tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term {\\it cold} implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. And the term {\\it atoms} means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are {\\it trapped} in the sense that they form a finite quantum system, though their number can be very large allowing for the use of the methods of statistical mechani","authors_text":"V.I. Yukalov","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-25T11:34:02Z","title":"Theory of Cold Atoms: Basics of Quantum Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6881","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:baa2dfe96eeb5a82009ee93cd92bd298e74abde75246ba7d76c873291fab160d","target":"record","created_at":"2026-05-18T01:50:21Z","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":"2a0f273ca19c02f5f5bdc15e80c05b0687a45b6c5bd57933c75b2b51c0557110","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-25T11:34:02Z","title_canon_sha256":"111b670f49a03e5a656258221a1f49fb8c551e954b8ac57194c9edc90a927924"},"schema_version":"1.0","source":{"id":"1304.6881","kind":"arxiv","version":1}},"canonical_sha256":"f183a65238049d36a5fe7c18de8bf138abf1c88a4dd7eb9e677097b258ccfc67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f183a65238049d36a5fe7c18de8bf138abf1c88a4dd7eb9e677097b258ccfc67","first_computed_at":"2026-05-18T01:50:21.972207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:21.972207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S4x/xLzQiN2KSIA4EvGaNsz3tnylcV99xIzkCsA88tOOPawfBo2uBbddgBtVJLeQZ/5ssulbQiTojmVrCsHqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:21.972980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa2dfe96eeb5a82009ee93cd92bd298e74abde75246ba7d76c873291fab160d","sha256:4ed57a665cc06ddb5c3b261a7a4693be15cd43845519c247e8a9ba0889b28587"],"state_sha256":"29e729894d0e7b8f2b03384b13492297dcd7fc755aaa17467b5a88976a32339a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0qD0uBxOeFH58jVppOF2MQJaQOQmbMOwlJt2Bs/ItTvdrmtJjZqZl3R+VYeo/3RiPR4xaEJ+HjYRrjg8BjoLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:04:19.995104Z","bundle_sha256":"941c821de3e3fd0e3ddb99f9b7d363d85141d84c342cccf844b57408bb0b50f0"}}