{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NCN7V7DEB2M2H5ARXXUMGSZISV","short_pith_number":"pith:NCN7V7DE","canonical_record":{"source":{"id":"math-ph/0508010","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-08-02T18:21:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"38bd5c8d318ab6c4f42de48d3260bcc9530d68c199d357c8dcb3763b9afce0dc","abstract_canon_sha256":"6816c7a72850422c5073061534f31d7adc97f8552151e169a098088b308407ee"},"schema_version":"1.0"},"canonical_sha256":"689bfafc640e99a3f411bde8c34b289543c620ff1676a877e819992ab5449576","source":{"kind":"arxiv","id":"math-ph/0508010","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0508010","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0508010v3","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0508010","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"NCN7V7DEB2M2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NCN7V7DEB2M2H5AR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NCN7V7DE","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NCN7V7DEB2M2H5ARXXUMGSZISV","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0508010","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-08-02T18:21:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"38bd5c8d318ab6c4f42de48d3260bcc9530d68c199d357c8dcb3763b9afce0dc","abstract_canon_sha256":"6816c7a72850422c5073061534f31d7adc97f8552151e169a098088b308407ee"},"schema_version":"1.0"},"canonical_sha256":"689bfafc640e99a3f411bde8c34b289543c620ff1676a877e819992ab5449576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:33.101046Z","signature_b64":"kICVTOLFzuQ6JoLW4CJB+IuwAjJoaPU3MMfJZdy1p4A5jhUFVG64TjWcUGfNmakyisHShAsAUW2jSPc4m8ZhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"689bfafc640e99a3f411bde8c34b289543c620ff1676a877e819992ab5449576","last_reissued_at":"2026-05-18T01:38:33.100362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:33.100362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0508010","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrN7wTiCT3PuMry786teSVQy1Vy79vz3bsAOum405+oxm2+htrUInycNHCJSac+qY2Gh4whFhMHUEsdocT1+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:02:34.316107Z"},"content_sha256":"e5f026cc6d51ce9ec7d46c328bd1434b497bd16b89cd60be5ca79a5b4c78b2ba","schema_version":"1.0","event_id":"sha256:e5f026cc6d51ce9ec7d46c328bd1434b497bd16b89cd60be5ca79a5b4c78b2ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NCN7V7DEB2M2H5ARXXUMGSZISV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of the Cubic Non-linear Schr\\\"odinger Equation from Quantum Dynamics of Many-Body Systems","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Schlein, Horng-Tzer Yau, Laszlo Erdos","submitted_at":"2005-08-02T18:21:55Z","abstract_excerpt":"We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schr\\\"odinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0508010","kind":"arxiv","version":3},"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":"2026-05-18T01:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1r2lx6KdkXOsnL3qD9LNVnk6ezfdZ06wHHxF3i++Uueo8EGmXLu2cZPheZpGxYcG6Fok/y77mnCikxuMSBpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:02:34.316476Z"},"content_sha256":"ae22236af2bb3c2e657842c5385c575dd9a2dafaed1ba81ffef81fcb9b587cec","schema_version":"1.0","event_id":"sha256:ae22236af2bb3c2e657842c5385c575dd9a2dafaed1ba81ffef81fcb9b587cec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/bundle.json","state_url":"https://pith.science/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/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":"2026-06-03T01:02:34Z","links":{"resolver":"https://pith.science/pith/NCN7V7DEB2M2H5ARXXUMGSZISV","bundle":"https://pith.science/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/bundle.json","state":"https://pith.science/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCN7V7DEB2M2H5ARXXUMGSZISV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NCN7V7DEB2M2H5ARXXUMGSZISV","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":"6816c7a72850422c5073061534f31d7adc97f8552151e169a098088b308407ee","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-08-02T18:21:55Z","title_canon_sha256":"38bd5c8d318ab6c4f42de48d3260bcc9530d68c199d357c8dcb3763b9afce0dc"},"schema_version":"1.0","source":{"id":"math-ph/0508010","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0508010","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0508010v3","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0508010","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"NCN7V7DEB2M2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NCN7V7DEB2M2H5AR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NCN7V7DE","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:ae22236af2bb3c2e657842c5385c575dd9a2dafaed1ba81ffef81fcb9b587cec","target":"graph","created_at":"2026-05-18T01:38:33Z","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 prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schr\\\"odinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$.","authors_text":"Benjamin Schlein, Horng-Tzer Yau, Laszlo Erdos","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-08-02T18:21:55Z","title":"Derivation of the Cubic Non-linear Schr\\\"odinger Equation from Quantum Dynamics of Many-Body Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0508010","kind":"arxiv","version":3},"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:e5f026cc6d51ce9ec7d46c328bd1434b497bd16b89cd60be5ca79a5b4c78b2ba","target":"record","created_at":"2026-05-18T01:38:33Z","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":"6816c7a72850422c5073061534f31d7adc97f8552151e169a098088b308407ee","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-08-02T18:21:55Z","title_canon_sha256":"38bd5c8d318ab6c4f42de48d3260bcc9530d68c199d357c8dcb3763b9afce0dc"},"schema_version":"1.0","source":{"id":"math-ph/0508010","kind":"arxiv","version":3}},"canonical_sha256":"689bfafc640e99a3f411bde8c34b289543c620ff1676a877e819992ab5449576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"689bfafc640e99a3f411bde8c34b289543c620ff1676a877e819992ab5449576","first_computed_at":"2026-05-18T01:38:33.100362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:33.100362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kICVTOLFzuQ6JoLW4CJB+IuwAjJoaPU3MMfJZdy1p4A5jhUFVG64TjWcUGfNmakyisHShAsAUW2jSPc4m8ZhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:33.101046Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0508010","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5f026cc6d51ce9ec7d46c328bd1434b497bd16b89cd60be5ca79a5b4c78b2ba","sha256:ae22236af2bb3c2e657842c5385c575dd9a2dafaed1ba81ffef81fcb9b587cec"],"state_sha256":"f42e37d146345372c311b711cc7ab3f725e3100441eebc5f44d3b0272ebd5232"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2GPgmUMVZWT0Nt9BPQ80aaRDx6KyOnKWDlazAREscJG7bE3D8SDGk8IAfzi8U1Y+3a2UCKyKBTmiGLFneJvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:02:34.318430Z","bundle_sha256":"7a73e3948212e24ca61fb4f28a528db4919249b23a74638bdd1687d719fb8baa"}}