{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DKNDBOOR6LVVOA2LJZDFBIEWQZ","short_pith_number":"pith:DKNDBOOR","canonical_record":{"source":{"id":"1011.4641","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-21T06:17:03Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"91043b09121fb1ecb52f486bcc6bf119c597ab0529277c475e81251ee7fe516e","abstract_canon_sha256":"2c02d347fc2888fff0ef71828368dc2b0881f43b633bf53086f7381d26c7b7ed"},"schema_version":"1.0"},"canonical_sha256":"1a9a30b9d1f2eb57034b4e4650a096864c84c3b805f0d903d23898c8eee64f1c","source":{"kind":"arxiv","id":"1011.4641","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4641","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4641v4","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4641","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"DKNDBOOR6LVV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DKNDBOOR6LVVOA2L","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DKNDBOOR","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DKNDBOOR6LVVOA2LJZDFBIEWQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4641","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-21T06:17:03Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"91043b09121fb1ecb52f486bcc6bf119c597ab0529277c475e81251ee7fe516e","abstract_canon_sha256":"2c02d347fc2888fff0ef71828368dc2b0881f43b633bf53086f7381d26c7b7ed"},"schema_version":"1.0"},"canonical_sha256":"1a9a30b9d1f2eb57034b4e4650a096864c84c3b805f0d903d23898c8eee64f1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:44.632751Z","signature_b64":"uyT0D7X3VEztFyVxlIpHJ3ov0yBVLNBelg+ZnFmbZUeAT1of8UztR5tWkyGOLVOQIwqNRTE/rcEEF7K8lN4oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a9a30b9d1f2eb57034b4e4650a096864c84c3b805f0d903d23898c8eee64f1c","last_reissued_at":"2026-05-18T02:56:44.632184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:44.632184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4641","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRwCPNKkPqmxIbm4ujno6qkJ0VFK+r0/pvF/lgiQhkzN65EoIzQa+UpIw2ZpwlNMq65/Ld6I+9Q2Qx7vNPXTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:42:34.164953Z"},"content_sha256":"4b30456a7e12cfc146c7637222e3a5b6b2604a65ae7d5669eced1d6f9007af89","schema_version":"1.0","event_id":"sha256:4b30456a7e12cfc146c7637222e3a5b6b2604a65ae7d5669eced1d6f9007af89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DKNDBOOR6LVVOA2LJZDFBIEWQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local well-posedness for Gross-Pitaevskii hierarchies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Zeqian Chen","submitted_at":"2010-11-21T06:17:03Z","abstract_excerpt":"We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local existence, uniqueness and stability of solutions. Explicit space-time type estimates for the solutions are obtained as well. In particular, this (F)-norm is compatible with the usual Sobolev space norm whenever the initial data is factorized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4641","kind":"arxiv","version":4},"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":"2026-05-18T02:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQ3+bywm1pzzOS78tW/XiAXriN37ogol7/08cgGuQwLdn4Im28laRRvtA8smx+DfHWb1tYuTp0LwbcNsj8HGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:42:34.165679Z"},"content_sha256":"c06820067b0851358dc348fdcad5d3fe82924f6b6469686a693e095746e36f27","schema_version":"1.0","event_id":"sha256:c06820067b0851358dc348fdcad5d3fe82924f6b6469686a693e095746e36f27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/bundle.json","state_url":"https://pith.science/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/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":"2026-06-09T03:42:34Z","links":{"resolver":"https://pith.science/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ","bundle":"https://pith.science/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/bundle.json","state":"https://pith.science/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKNDBOOR6LVVOA2LJZDFBIEWQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DKNDBOOR6LVVOA2LJZDFBIEWQZ","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":"2c02d347fc2888fff0ef71828368dc2b0881f43b633bf53086f7381d26c7b7ed","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-21T06:17:03Z","title_canon_sha256":"91043b09121fb1ecb52f486bcc6bf119c597ab0529277c475e81251ee7fe516e"},"schema_version":"1.0","source":{"id":"1011.4641","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4641","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4641v4","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4641","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"DKNDBOOR6LVV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DKNDBOOR6LVVOA2L","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DKNDBOOR","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c06820067b0851358dc348fdcad5d3fe82924f6b6469686a693e095746e36f27","target":"graph","created_at":"2026-05-18T02:56:44Z","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 Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local existence, uniqueness and stability of solutions. Explicit space-time type estimates for the solutions are obtained as well. In particular, this (F)-norm is compatible with the usual Sobolev space norm whenever the initial data is factorized.","authors_text":"Zeqian Chen","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-21T06:17:03Z","title":"Local well-posedness for Gross-Pitaevskii hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4641","kind":"arxiv","version":4},"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":"sha256:4b30456a7e12cfc146c7637222e3a5b6b2604a65ae7d5669eced1d6f9007af89","target":"record","created_at":"2026-05-18T02:56:44Z","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":"2c02d347fc2888fff0ef71828368dc2b0881f43b633bf53086f7381d26c7b7ed","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-21T06:17:03Z","title_canon_sha256":"91043b09121fb1ecb52f486bcc6bf119c597ab0529277c475e81251ee7fe516e"},"schema_version":"1.0","source":{"id":"1011.4641","kind":"arxiv","version":4}},"canonical_sha256":"1a9a30b9d1f2eb57034b4e4650a096864c84c3b805f0d903d23898c8eee64f1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a9a30b9d1f2eb57034b4e4650a096864c84c3b805f0d903d23898c8eee64f1c","first_computed_at":"2026-05-18T02:56:44.632184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:44.632184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uyT0D7X3VEztFyVxlIpHJ3ov0yBVLNBelg+ZnFmbZUeAT1of8UztR5tWkyGOLVOQIwqNRTE/rcEEF7K8lN4oAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:44.632751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4641","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b30456a7e12cfc146c7637222e3a5b6b2604a65ae7d5669eced1d6f9007af89","sha256:c06820067b0851358dc348fdcad5d3fe82924f6b6469686a693e095746e36f27"],"state_sha256":"22cb28e148f84b343ae15ca8643730438988560e03a6a04c21012461ef1fbcdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F93z4fNdzamX334QNLCRMtcL5qw0r87mHUC6teAshCAHNkyGSVxq6z+Dx+6EYIdQ1ztrWDJfEnKHVMVU6snLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:42:34.169709Z","bundle_sha256":"011a52058b22dd1c9761ba74e63ad733be3c11d0b632ab05407e327ef684fab2"}}