{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZD4YYTNQOVHIWOV6DLXL4CQZHD","short_pith_number":"pith:ZD4YYTNQ","canonical_record":{"source":{"id":"1104.0138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-01T10:49:32Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"56aaba5916ae27d4097aab288cbd8b7844cbc441055504951fbc7ebeacb59aad","abstract_canon_sha256":"72c5439a26c907cbcdea3dfe5253e429cc3cfd3e75ba854af0fa0d607034dfb8"},"schema_version":"1.0"},"canonical_sha256":"c8f98c4db0754e8b3abe1aeebe0a1938ce19da69a8015031811e87f2dea58fc5","source":{"kind":"arxiv","id":"1104.0138","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0138","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0138v1","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0138","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZD4YYTNQOVHI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZD4YYTNQOVHIWOV6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZD4YYTNQ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZD4YYTNQOVHIWOV6DLXL4CQZHD","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-01T10:49:32Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"56aaba5916ae27d4097aab288cbd8b7844cbc441055504951fbc7ebeacb59aad","abstract_canon_sha256":"72c5439a26c907cbcdea3dfe5253e429cc3cfd3e75ba854af0fa0d607034dfb8"},"schema_version":"1.0"},"canonical_sha256":"c8f98c4db0754e8b3abe1aeebe0a1938ce19da69a8015031811e87f2dea58fc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:12.295257Z","signature_b64":"QuwkAx6SOd/1ydEQjIAcmL2fit8q+t5Fm5gg/hCN2OY8dcmP+NZfAm1F5AhtpWDdPuHU+hfufHlv/NxpDgnQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8f98c4db0754e8b3abe1aeebe0a1938ce19da69a8015031811e87f2dea58fc5","last_reissued_at":"2026-05-18T04:25:12.294713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:12.294713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0138","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":"2026-05-18T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4eBY3g/ExlU2J6kbbBba68KI+rpAbB/0wMN3v6XW6KG2mUiEPuYalmI9IHPmFQLyfziMB7XR/HGwq1F47HbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:07:06.889724Z"},"content_sha256":"a1fa2905249885782eab7eda4ec7aa7b4db9e7c990e2bc57ee75b24535c5690f","schema_version":"1.0","event_id":"sha256:a1fa2905249885782eab7eda4ec7aa7b4db9e7c990e2bc57ee75b24535c5690f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZD4YYTNQOVHIWOV6DLXL4CQZHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of Nonlinear Schr\\\"{o}dinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Bai-Jun Zhang, Li-Xiao, Qing-Cai Wang, Shuang Cheng, Xiang-Yao Wu, Xiao-jing Liu, Yan-Wang, Yi-Heng Wu","submitted_at":"2011-04-01T10:49:32Z","abstract_excerpt":"We propose some nonlinear Schr\\\"{o}dinger equations by adding some higher order terms to the Lagrangian density of Schr\\\"{o}dinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schr\\\"{o}dinger equation is weak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0138","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":"2026-05-18T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wql1KcLynZtTr1KKk1PGgJ2FrG9vVluuSU+4vwQL/OJd440B6h9r2VCr5RrinD1y8xB/Tz5W01tzZVfAYZyCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:07:06.890071Z"},"content_sha256":"1471a5544d9aae2dde497ea2a65f413915c57a3fe05d292948bd55188d00b019","schema_version":"1.0","event_id":"sha256:1471a5544d9aae2dde497ea2a65f413915c57a3fe05d292948bd55188d00b019"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/bundle.json","state_url":"https://pith.science/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/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":"2026-06-04T09:07:06Z","links":{"resolver":"https://pith.science/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD","bundle":"https://pith.science/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/bundle.json","state":"https://pith.science/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD4YYTNQOVHIWOV6DLXL4CQZHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZD4YYTNQOVHIWOV6DLXL4CQZHD","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":"72c5439a26c907cbcdea3dfe5253e429cc3cfd3e75ba854af0fa0d607034dfb8","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-01T10:49:32Z","title_canon_sha256":"56aaba5916ae27d4097aab288cbd8b7844cbc441055504951fbc7ebeacb59aad"},"schema_version":"1.0","source":{"id":"1104.0138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0138","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0138v1","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0138","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZD4YYTNQOVHI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZD4YYTNQOVHIWOV6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZD4YYTNQ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1471a5544d9aae2dde497ea2a65f413915c57a3fe05d292948bd55188d00b019","target":"graph","created_at":"2026-05-18T04:25:12Z","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 propose some nonlinear Schr\\\"{o}dinger equations by adding some higher order terms to the Lagrangian density of Schr\\\"{o}dinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schr\\\"{o}dinger equation is weak.","authors_text":"Bai-Jun Zhang, Li-Xiao, Qing-Cai Wang, Shuang Cheng, Xiang-Yao Wu, Xiao-jing Liu, Yan-Wang, Yi-Heng Wu","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-01T10:49:32Z","title":"Derivation of Nonlinear Schr\\\"{o}dinger Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0138","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:a1fa2905249885782eab7eda4ec7aa7b4db9e7c990e2bc57ee75b24535c5690f","target":"record","created_at":"2026-05-18T04:25:12Z","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":"72c5439a26c907cbcdea3dfe5253e429cc3cfd3e75ba854af0fa0d607034dfb8","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-01T10:49:32Z","title_canon_sha256":"56aaba5916ae27d4097aab288cbd8b7844cbc441055504951fbc7ebeacb59aad"},"schema_version":"1.0","source":{"id":"1104.0138","kind":"arxiv","version":1}},"canonical_sha256":"c8f98c4db0754e8b3abe1aeebe0a1938ce19da69a8015031811e87f2dea58fc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f98c4db0754e8b3abe1aeebe0a1938ce19da69a8015031811e87f2dea58fc5","first_computed_at":"2026-05-18T04:25:12.294713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:12.294713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuwkAx6SOd/1ydEQjIAcmL2fit8q+t5Fm5gg/hCN2OY8dcmP+NZfAm1F5AhtpWDdPuHU+hfufHlv/NxpDgnQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:12.295257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1fa2905249885782eab7eda4ec7aa7b4db9e7c990e2bc57ee75b24535c5690f","sha256:1471a5544d9aae2dde497ea2a65f413915c57a3fe05d292948bd55188d00b019"],"state_sha256":"deaca2719af0d8db843f03707dbb42b99dcd9aa53cc9f66faf2403d781207449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urF/0gmqvgx9BdOGvd5zwbMyNgim3DPU4DiBQd1Ey7Bjq/6m8imYGbeADCVfEtwg1wXnyOtG3Xd6E1XUJNsxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T09:07:06.892069Z","bundle_sha256":"f4065a56afcb6357d4a6bca5b1a82f5071be30ca1e2da2506c22d15ec3d40988"}}