{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JMOIFEZXFWDBOXV5727EQEFA7S","short_pith_number":"pith:JMOIFEZX","canonical_record":{"source":{"id":"1109.2875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-13T18:24:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3147c2283ed6a07a91121046a75d71109d4bfc6816de61146902fbd0a6db479","abstract_canon_sha256":"2b8a946a85b1333b865abea83eb0503ddbd3ba31a2631496c34e6fa08b936fb7"},"schema_version":"1.0"},"canonical_sha256":"4b1c8293372d86175ebdfebe4810a0fcaa7295e35f46cc0288111384a04bcc70","source":{"kind":"arxiv","id":"1109.2875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2875","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2875v1","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2875","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"pith_short_12","alias_value":"JMOIFEZXFWDB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JMOIFEZXFWDBOXV5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JMOIFEZX","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JMOIFEZXFWDBOXV5727EQEFA7S","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-13T18:24:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3147c2283ed6a07a91121046a75d71109d4bfc6816de61146902fbd0a6db479","abstract_canon_sha256":"2b8a946a85b1333b865abea83eb0503ddbd3ba31a2631496c34e6fa08b936fb7"},"schema_version":"1.0"},"canonical_sha256":"4b1c8293372d86175ebdfebe4810a0fcaa7295e35f46cc0288111384a04bcc70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:07.508919Z","signature_b64":"H+7etlh9D3tK2YWL//5qu6xff7j2faHzfIimd7/bIy6V73wbZWTr9PqWN/0g+ekdRwPsYUFsV7ybPkM+OnfoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b1c8293372d86175ebdfebe4810a0fcaa7295e35f46cc0288111384a04bcc70","last_reissued_at":"2026-05-18T04:13:07.508427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:07.508427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2875","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":"2026-05-18T04:13:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gd41YQCIXJyoGBoccpEriVrUXn5UOEENRUOad81SJNztgSEUdA9e+e9NicQcwUVcuIHKw7T1D32rOD8ZToQQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:23:49.787351Z"},"content_sha256":"438e36582a1c50442d362a9171c2d202431c9607b22f6e916eb56c22b68e3792","schema_version":"1.0","event_id":"sha256:438e36582a1c50442d362a9171c2d202431c9607b22f6e916eb56c22b68e3792"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JMOIFEZXFWDBOXV5727EQEFA7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bogoliubov theory and bosonic atoms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Phan Thanh Nam","submitted_at":"2011-09-13T18:24:10Z","abstract_excerpt":"We formulate the Bogoliubov variational principle in a mathematical framework similar to the generalized Hartree-Fock theory. Then we analyze the Bogoliubov theory for bosonic atoms in details. We discuss heuristically why the Bogoliubov energy should give the first correction to the leading energy of large bosonic atoms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2875","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":"2026-05-18T04:13:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wwWwHl4ytNjD5oxhFX7Z0q4eHjA3sg1p/WLLW7NkCj5pmG4NJaN8i3LomUI7cMSzJkHuEHQvyeJ54ATXj+1bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:23:49.787708Z"},"content_sha256":"b8769592e5068fde8bff0eb907e08f69271393052d73a7a9433dcc347bac0ef1","schema_version":"1.0","event_id":"sha256:b8769592e5068fde8bff0eb907e08f69271393052d73a7a9433dcc347bac0ef1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMOIFEZXFWDBOXV5727EQEFA7S/bundle.json","state_url":"https://pith.science/pith/JMOIFEZXFWDBOXV5727EQEFA7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMOIFEZXFWDBOXV5727EQEFA7S/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":"2026-05-28T03:23:49Z","links":{"resolver":"https://pith.science/pith/JMOIFEZXFWDBOXV5727EQEFA7S","bundle":"https://pith.science/pith/JMOIFEZXFWDBOXV5727EQEFA7S/bundle.json","state":"https://pith.science/pith/JMOIFEZXFWDBOXV5727EQEFA7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMOIFEZXFWDBOXV5727EQEFA7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JMOIFEZXFWDBOXV5727EQEFA7S","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":"2b8a946a85b1333b865abea83eb0503ddbd3ba31a2631496c34e6fa08b936fb7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-13T18:24:10Z","title_canon_sha256":"a3147c2283ed6a07a91121046a75d71109d4bfc6816de61146902fbd0a6db479"},"schema_version":"1.0","source":{"id":"1109.2875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2875","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2875v1","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2875","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"pith_short_12","alias_value":"JMOIFEZXFWDB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JMOIFEZXFWDBOXV5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JMOIFEZX","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:b8769592e5068fde8bff0eb907e08f69271393052d73a7a9433dcc347bac0ef1","target":"graph","created_at":"2026-05-18T04:13:07Z","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 formulate the Bogoliubov variational principle in a mathematical framework similar to the generalized Hartree-Fock theory. Then we analyze the Bogoliubov theory for bosonic atoms in details. We discuss heuristically why the Bogoliubov energy should give the first correction to the leading energy of large bosonic atoms.","authors_text":"Phan Thanh Nam","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-13T18:24:10Z","title":"Bogoliubov theory and bosonic atoms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2875","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":"sha256:438e36582a1c50442d362a9171c2d202431c9607b22f6e916eb56c22b68e3792","target":"record","created_at":"2026-05-18T04:13:07Z","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":"2b8a946a85b1333b865abea83eb0503ddbd3ba31a2631496c34e6fa08b936fb7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-13T18:24:10Z","title_canon_sha256":"a3147c2283ed6a07a91121046a75d71109d4bfc6816de61146902fbd0a6db479"},"schema_version":"1.0","source":{"id":"1109.2875","kind":"arxiv","version":1}},"canonical_sha256":"4b1c8293372d86175ebdfebe4810a0fcaa7295e35f46cc0288111384a04bcc70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b1c8293372d86175ebdfebe4810a0fcaa7295e35f46cc0288111384a04bcc70","first_computed_at":"2026-05-18T04:13:07.508427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:07.508427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H+7etlh9D3tK2YWL//5qu6xff7j2faHzfIimd7/bIy6V73wbZWTr9PqWN/0g+ekdRwPsYUFsV7ybPkM+OnfoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:07.508919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:438e36582a1c50442d362a9171c2d202431c9607b22f6e916eb56c22b68e3792","sha256:b8769592e5068fde8bff0eb907e08f69271393052d73a7a9433dcc347bac0ef1"],"state_sha256":"492696d3ec60c6ea24c589b02e685b7d794e70387d2bd452ccdce54d35b03e31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PU5fPPYVgzvtkD3NPZ3h43RGabAsgKUUoF7yjrTsxuivVsPl9CDBAT0K/S7lEOx6ktxmSgBpy4/L2ELUsPqoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:23:49.789762Z","bundle_sha256":"95f1c1dd685cd73bf0656be656805cb8fb8b1b314ccda75c72084f728333f5db"}}