{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JM5QBW7AH2BJVATAUF74IEDPCV","short_pith_number":"pith:JM5QBW7A","canonical_record":{"source":{"id":"1309.1702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-06T17:28:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"02c22dbb69d266c66b36b9ae86636629d445edadd5e45d89eed31a3a0be69993","abstract_canon_sha256":"0b917764f141073a7c0c22d5629f3a81a03aab7c4c1d138b88f33375e0f14378"},"schema_version":"1.0"},"canonical_sha256":"4b3b00dbe03e829a8260a17fc4106f15665ff606d5cce143e187e545a1bd5f95","source":{"kind":"arxiv","id":"1309.1702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1702","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1702v1","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1702","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"JM5QBW7AH2BJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JM5QBW7AH2BJVATA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JM5QBW7A","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JM5QBW7AH2BJVATAUF74IEDPCV","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-06T17:28:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"02c22dbb69d266c66b36b9ae86636629d445edadd5e45d89eed31a3a0be69993","abstract_canon_sha256":"0b917764f141073a7c0c22d5629f3a81a03aab7c4c1d138b88f33375e0f14378"},"schema_version":"1.0"},"canonical_sha256":"4b3b00dbe03e829a8260a17fc4106f15665ff606d5cce143e187e545a1bd5f95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:58.512960Z","signature_b64":"cUlbMrOsEIM9TbRJOThSLRoE5FhxElqW0V/s3lMK0rHRRgAJbX8YDH3TzLbQ+1yf0mdyCwS41lXLeNFrsgzHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b3b00dbe03e829a8260a17fc4106f15665ff606d5cce143e187e545a1bd5f95","last_reissued_at":"2026-05-18T03:00:58.512449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:58.512449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1702","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":"2026-05-18T03:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYGcbX6RSheMIL7JCTUh94zfQXoBNTYo7p/3PKsziKjjpOWvAg7NL3GyS0RorddAbstciv6Pxhv50VXm2CvbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:36:42.698919Z"},"content_sha256":"d416b971dc9e5f5de6f906fd2171d2855e97fc4498286aa950627d13e4f4eabf","schema_version":"1.0","event_id":"sha256:d416b971dc9e5f5de6f906fd2171d2855e97fc4498286aa950627d13e4f4eabf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JM5QBW7AH2BJVATAUF74IEDPCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Central Limit Theorem in Quantum Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Schlein, Chiara Saffirio, Simon Buchholz","submitted_at":"2013-09-06T17:28:18Z","abstract_excerpt":"We consider the time evolution of $N$ bosons in the mean field regime for factorized initial data. In the limit of large $N$, the many body evolution can be approximated by the non-linear Hartree equation. In this paper we are interested in the fluctuations around the Hartree dynamics. We choose $k$ self-adjoint one-particle operators $O_1, \\dots, O_k$ on $L^2 (\\R^3)$, and we average their action over the $N$-particles. We show that, for every fixed $t \\in \\R$, expectations of products of functions of the averaged observables approach, as $N \\to \\infty$, expectations with respect to a complex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1702","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":"2026-05-18T03:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+JPI68jSbEws1Ey5YYqnPi+TqF3wJFfqifF7sGFsGtNiQKeOHTax2Q6xpFlLvv6cxWkZCS32KtYCGybCcjP8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:36:42.699260Z"},"content_sha256":"43cc9ce817575fa42241c77b9e73ed6697408a9a342dd3b5cf21cf49dc480832","schema_version":"1.0","event_id":"sha256:43cc9ce817575fa42241c77b9e73ed6697408a9a342dd3b5cf21cf49dc480832"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JM5QBW7AH2BJVATAUF74IEDPCV/bundle.json","state_url":"https://pith.science/pith/JM5QBW7AH2BJVATAUF74IEDPCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JM5QBW7AH2BJVATAUF74IEDPCV/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":"2026-06-03T03:36:42Z","links":{"resolver":"https://pith.science/pith/JM5QBW7AH2BJVATAUF74IEDPCV","bundle":"https://pith.science/pith/JM5QBW7AH2BJVATAUF74IEDPCV/bundle.json","state":"https://pith.science/pith/JM5QBW7AH2BJVATAUF74IEDPCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JM5QBW7AH2BJVATAUF74IEDPCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JM5QBW7AH2BJVATAUF74IEDPCV","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":"0b917764f141073a7c0c22d5629f3a81a03aab7c4c1d138b88f33375e0f14378","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-06T17:28:18Z","title_canon_sha256":"02c22dbb69d266c66b36b9ae86636629d445edadd5e45d89eed31a3a0be69993"},"schema_version":"1.0","source":{"id":"1309.1702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1702","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1702v1","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1702","created_at":"2026-05-18T03:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"JM5QBW7AH2BJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JM5QBW7AH2BJVATA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JM5QBW7A","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:43cc9ce817575fa42241c77b9e73ed6697408a9a342dd3b5cf21cf49dc480832","target":"graph","created_at":"2026-05-18T03:00:58Z","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 consider the time evolution of $N$ bosons in the mean field regime for factorized initial data. In the limit of large $N$, the many body evolution can be approximated by the non-linear Hartree equation. In this paper we are interested in the fluctuations around the Hartree dynamics. We choose $k$ self-adjoint one-particle operators $O_1, \\dots, O_k$ on $L^2 (\\R^3)$, and we average their action over the $N$-particles. We show that, for every fixed $t \\in \\R$, expectations of products of functions of the averaged observables approach, as $N \\to \\infty$, expectations with respect to a complex ","authors_text":"Benjamin Schlein, Chiara Saffirio, Simon Buchholz","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-06T17:28:18Z","title":"Multivariate Central Limit Theorem in Quantum Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1702","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:d416b971dc9e5f5de6f906fd2171d2855e97fc4498286aa950627d13e4f4eabf","target":"record","created_at":"2026-05-18T03:00:58Z","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":"0b917764f141073a7c0c22d5629f3a81a03aab7c4c1d138b88f33375e0f14378","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-06T17:28:18Z","title_canon_sha256":"02c22dbb69d266c66b36b9ae86636629d445edadd5e45d89eed31a3a0be69993"},"schema_version":"1.0","source":{"id":"1309.1702","kind":"arxiv","version":1}},"canonical_sha256":"4b3b00dbe03e829a8260a17fc4106f15665ff606d5cce143e187e545a1bd5f95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b3b00dbe03e829a8260a17fc4106f15665ff606d5cce143e187e545a1bd5f95","first_computed_at":"2026-05-18T03:00:58.512449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:58.512449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUlbMrOsEIM9TbRJOThSLRoE5FhxElqW0V/s3lMK0rHRRgAJbX8YDH3TzLbQ+1yf0mdyCwS41lXLeNFrsgzHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:58.512960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d416b971dc9e5f5de6f906fd2171d2855e97fc4498286aa950627d13e4f4eabf","sha256:43cc9ce817575fa42241c77b9e73ed6697408a9a342dd3b5cf21cf49dc480832"],"state_sha256":"f89ccb4de86697943351ee641d4462834385cb2d41dbf7e4a841b614b6b06577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaYNFFwpsfAa4ya2omwb/zBIwQliqTiYG2Cjg2k09CNkbHEzFZs4ijAAk4r6DVv6zYcrTJdrvLjfvbZRjlr2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:36:42.701152Z","bundle_sha256":"2e38abd5670072f4ddea5213de66511825d126c21811b4d31c470024f1604494"}}