{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RC2463RB3YYKUGUBM36NYDDHG2","short_pith_number":"pith:RC2463RB","canonical_record":{"source":{"id":"1409.1425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T12:50:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"36367b59932abab581711f9739f606fa88f11111e0f91e2019ab25a13ad39001","abstract_canon_sha256":"38351e8de116dc47968a6ecafdc0b4c11d6d3533fdf506d2eb3dcd5dbc0401a3"},"schema_version":"1.0"},"canonical_sha256":"88b5cf6e21de30aa1a8166fcdc0c6736b634ca3bdf09246db88e0e5514fb2c50","source":{"kind":"arxiv","id":"1409.1425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1425","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1425v1","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1425","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"RC2463RB3YYK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RC2463RB3YYKUGUB","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RC2463RB","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RC2463RB3YYKUGUBM36NYDDHG2","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T12:50:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"36367b59932abab581711f9739f606fa88f11111e0f91e2019ab25a13ad39001","abstract_canon_sha256":"38351e8de116dc47968a6ecafdc0b4c11d6d3533fdf506d2eb3dcd5dbc0401a3"},"schema_version":"1.0"},"canonical_sha256":"88b5cf6e21de30aa1a8166fcdc0c6736b634ca3bdf09246db88e0e5514fb2c50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:37.505613Z","signature_b64":"h+iksnIZuHuIQUAWTNhghqnYIsfXD9rvh+aZgigMYan95BQIqfh0LT5sHqU4XaX/o2as2k2TlyjjReVUPUYDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88b5cf6e21de30aa1a8166fcdc0c6736b634ca3bdf09246db88e0e5514fb2c50","last_reissued_at":"2026-05-18T01:11:37.505239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:37.505239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1425","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":"2026-05-18T01:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eix4NiaZsj9VnPfed3HjNTOPkoHrTuGQVfBKwz61E/UkfhpAeY2Ls1MIXDRViFByuACAMYoRUSeXA7HThUXECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:08:09.021331Z"},"content_sha256":"8a7aa5a4984dc802c55d1acfb23f64505fbf1a5ab7d74a562972b64321d1e700","schema_version":"1.0","event_id":"sha256:8a7aa5a4984dc802c55d1acfb23f64505fbf1a5ab7d74a562972b64321d1e700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RC2463RB3YYKUGUBM36NYDDHG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Justin Holmer, Xuwen Chen","submitted_at":"2014-09-04T12:50:44Z","abstract_excerpt":"We consider the dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\\beta -1}V(N^{\\beta }\\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into account all of the interparticle singular correlation structures developed by the many-body evolution from the beginning. Assuming energy conditions on the $N$-body wave function, for $\\beta \\in \\left( 0,1\\right] $, we derive the Gross-Pitaevskii hierarchy with $2$-body interaction. In particular, we establish that, in the $N\\rightarrow \\infty $ limit, all $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1425","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":"2026-05-18T01:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4xI9sVCF0az1ep2DYM3l3JKR9DENz74LYgqeq09z7MbFRuE8QoYnCpuyfGYjDPlfVvbTTTWWKyoFFiY5qlOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:08:09.022046Z"},"content_sha256":"3eda11a75267ee1d23b2407bd891d14ce42876d2dd39c0929152c51cb3e3be65","schema_version":"1.0","event_id":"sha256:3eda11a75267ee1d23b2407bd891d14ce42876d2dd39c0929152c51cb3e3be65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RC2463RB3YYKUGUBM36NYDDHG2/bundle.json","state_url":"https://pith.science/pith/RC2463RB3YYKUGUBM36NYDDHG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RC2463RB3YYKUGUBM36NYDDHG2/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":"2026-05-23T19:08:09Z","links":{"resolver":"https://pith.science/pith/RC2463RB3YYKUGUBM36NYDDHG2","bundle":"https://pith.science/pith/RC2463RB3YYKUGUBM36NYDDHG2/bundle.json","state":"https://pith.science/pith/RC2463RB3YYKUGUBM36NYDDHG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RC2463RB3YYKUGUBM36NYDDHG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RC2463RB3YYKUGUBM36NYDDHG2","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":"38351e8de116dc47968a6ecafdc0b4c11d6d3533fdf506d2eb3dcd5dbc0401a3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T12:50:44Z","title_canon_sha256":"36367b59932abab581711f9739f606fa88f11111e0f91e2019ab25a13ad39001"},"schema_version":"1.0","source":{"id":"1409.1425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1425","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1425v1","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1425","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"RC2463RB3YYK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RC2463RB3YYKUGUB","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RC2463RB","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:3eda11a75267ee1d23b2407bd891d14ce42876d2dd39c0929152c51cb3e3be65","target":"graph","created_at":"2026-05-18T01:11:37Z","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 dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\\beta -1}V(N^{\\beta }\\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into account all of the interparticle singular correlation structures developed by the many-body evolution from the beginning. Assuming energy conditions on the $N$-body wave function, for $\\beta \\in \\left( 0,1\\right] $, we derive the Gross-Pitaevskii hierarchy with $2$-body interaction. In particular, we establish that, in the $N\\rightarrow \\infty $ limit, all $k","authors_text":"Justin Holmer, Xuwen Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T12:50:44Z","title":"Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1425","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":"sha256:8a7aa5a4984dc802c55d1acfb23f64505fbf1a5ab7d74a562972b64321d1e700","target":"record","created_at":"2026-05-18T01:11:37Z","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":"38351e8de116dc47968a6ecafdc0b4c11d6d3533fdf506d2eb3dcd5dbc0401a3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T12:50:44Z","title_canon_sha256":"36367b59932abab581711f9739f606fa88f11111e0f91e2019ab25a13ad39001"},"schema_version":"1.0","source":{"id":"1409.1425","kind":"arxiv","version":1}},"canonical_sha256":"88b5cf6e21de30aa1a8166fcdc0c6736b634ca3bdf09246db88e0e5514fb2c50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b5cf6e21de30aa1a8166fcdc0c6736b634ca3bdf09246db88e0e5514fb2c50","first_computed_at":"2026-05-18T01:11:37.505239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:37.505239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h+iksnIZuHuIQUAWTNhghqnYIsfXD9rvh+aZgigMYan95BQIqfh0LT5sHqU4XaX/o2as2k2TlyjjReVUPUYDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:37.505613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a7aa5a4984dc802c55d1acfb23f64505fbf1a5ab7d74a562972b64321d1e700","sha256:3eda11a75267ee1d23b2407bd891d14ce42876d2dd39c0929152c51cb3e3be65"],"state_sha256":"0ee00e62fb2ee0297f62f8afea8f24e8c3e397afd63b09c52968a9c013afcf0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAHXPTgyJUHj8f4ZKhhh7trEp/k2GN5mffGFQLpse1mNV/eIapJD9VZCaDuirkFxrTLiO0kEBY6N/0bZJoPiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T19:08:09.024976Z","bundle_sha256":"f549d36bf5251eeeb936256cca78b1f85237877d90e6ed45eaccb6928ee04bc2"}}