{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JP4M6H2AUTUWB2M3HWHQLYVOVC","short_pith_number":"pith:JP4M6H2A","canonical_record":{"source":{"id":"1902.10254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T22:37:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a8cb33939cb773a9f695ce857393874048b5f1b5a0681a2623e8c343f4e35eac","abstract_canon_sha256":"58b3b477103a9a90d3bb077c1fcbb7505dfcfa0e9b978d64bac1411422595e7f"},"schema_version":"1.0"},"canonical_sha256":"4bf8cf1f40a4e960e99b3d8f05e2aea89cd67db4def5e47cb2db827247341e56","source":{"kind":"arxiv","id":"1902.10254","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10254","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10254v2","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10254","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"JP4M6H2AUTUW","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_16","alias_value":"JP4M6H2AUTUWB2M3","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_8","alias_value":"JP4M6H2A","created_at":"2026-06-04T20:13:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JP4M6H2AUTUWB2M3HWHQLYVOVC","target":"record","payload":{"canonical_record":{"source":{"id":"1902.10254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T22:37:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a8cb33939cb773a9f695ce857393874048b5f1b5a0681a2623e8c343f4e35eac","abstract_canon_sha256":"58b3b477103a9a90d3bb077c1fcbb7505dfcfa0e9b978d64bac1411422595e7f"},"schema_version":"1.0"},"canonical_sha256":"4bf8cf1f40a4e960e99b3d8f05e2aea89cd67db4def5e47cb2db827247341e56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:56.773621Z","signature_b64":"qXUHMGjoumbY+VR8mejv/ghHEKbwLqVDkomEJvI92KtcSAImoknQl3TI5AVMB+jaeoNfe0IngFstFDJQ1q2wAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bf8cf1f40a4e960e99b3d8f05e2aea89cd67db4def5e47cb2db827247341e56","last_reissued_at":"2026-06-04T20:13:56.773140Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:56.773140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.10254","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T20:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LT/Kg8j7/tFZ7LrVkCSwVpIY5PcyMX61NHMKb1G9aexDSgx97YCDRpKUZQicYwez9fKD/0wGBCDtDxVoWSs6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:05:36.876834Z"},"content_sha256":"b68d938293b3369355bf6a0dbb90280af8a14a2800f3262bf7032c82025283fb","schema_version":"1.0","event_id":"sha256:b68d938293b3369355bf6a0dbb90280af8a14a2800f3262bf7032c82025283fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JP4M6H2AUTUWB2M3HWHQLYVOVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mass- and energy-conserved numerical schemes for nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hailiang Liu, Shu Ma, Xiaobing Feng","submitted_at":"2019-02-26T22:37:30Z","abstract_excerpt":"In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schr\\\"odinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error analyses are provided for each proposed scheme. Efficient fixed-point iterative solvers are also constructed to solve the resulting nonlinear discrete problems. As a byproduct, an efficient one-step implementation of the BDF schemes is obtained as well. Extensive numerical experiments are presented to demonstrate the convergence and the capability of capturing the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10254","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.10254/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T20:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NTVij9zJQ7y9ZBuy3DVgzlS3+xWZvUt15cUkZCkShE+eZ0JYOphzJyU+c8jJq94GTwxKggduvfl2R1xCdkoiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:05:36.877221Z"},"content_sha256":"91a68708fb2122a78759d2fb25910afea6592f73d58bf89bb0aca6c77490247c","schema_version":"1.0","event_id":"sha256:91a68708fb2122a78759d2fb25910afea6592f73d58bf89bb0aca6c77490247c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/bundle.json","state_url":"https://pith.science/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/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":"2026-06-20T22:05:36Z","links":{"resolver":"https://pith.science/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC","bundle":"https://pith.science/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/bundle.json","state":"https://pith.science/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JP4M6H2AUTUWB2M3HWHQLYVOVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JP4M6H2AUTUWB2M3HWHQLYVOVC","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":"58b3b477103a9a90d3bb077c1fcbb7505dfcfa0e9b978d64bac1411422595e7f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T22:37:30Z","title_canon_sha256":"a8cb33939cb773a9f695ce857393874048b5f1b5a0681a2623e8c343f4e35eac"},"schema_version":"1.0","source":{"id":"1902.10254","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10254","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10254v2","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10254","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"JP4M6H2AUTUW","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_16","alias_value":"JP4M6H2AUTUWB2M3","created_at":"2026-06-04T20:13:56Z"},{"alias_kind":"pith_short_8","alias_value":"JP4M6H2A","created_at":"2026-06-04T20:13:56Z"}],"graph_snapshots":[{"event_id":"sha256:91a68708fb2122a78759d2fb25910afea6592f73d58bf89bb0aca6c77490247c","target":"graph","created_at":"2026-06-04T20:13:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.10254/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schr\\\"odinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error analyses are provided for each proposed scheme. Efficient fixed-point iterative solvers are also constructed to solve the resulting nonlinear discrete problems. As a byproduct, an efficient one-step implementation of the BDF schemes is obtained as well. Extensive numerical experiments are presented to demonstrate the convergence and the capability of capturing the","authors_text":"Hailiang Liu, Shu Ma, Xiaobing Feng","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T22:37:30Z","title":"Mass- and energy-conserved numerical schemes for nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10254","kind":"arxiv","version":2},"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:b68d938293b3369355bf6a0dbb90280af8a14a2800f3262bf7032c82025283fb","target":"record","created_at":"2026-06-04T20:13:56Z","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":"58b3b477103a9a90d3bb077c1fcbb7505dfcfa0e9b978d64bac1411422595e7f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-26T22:37:30Z","title_canon_sha256":"a8cb33939cb773a9f695ce857393874048b5f1b5a0681a2623e8c343f4e35eac"},"schema_version":"1.0","source":{"id":"1902.10254","kind":"arxiv","version":2}},"canonical_sha256":"4bf8cf1f40a4e960e99b3d8f05e2aea89cd67db4def5e47cb2db827247341e56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bf8cf1f40a4e960e99b3d8f05e2aea89cd67db4def5e47cb2db827247341e56","first_computed_at":"2026-06-04T20:13:56.773140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:56.773140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qXUHMGjoumbY+VR8mejv/ghHEKbwLqVDkomEJvI92KtcSAImoknQl3TI5AVMB+jaeoNfe0IngFstFDJQ1q2wAw==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:56.773621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10254","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b68d938293b3369355bf6a0dbb90280af8a14a2800f3262bf7032c82025283fb","sha256:91a68708fb2122a78759d2fb25910afea6592f73d58bf89bb0aca6c77490247c"],"state_sha256":"9f7a2a4083ee9ae83d31a92dcd0b4248dc17bceb2dae2c59c41a87269809b25a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5I3AWADAJJI+tqmeh03uGLlnrur+x8F26OZjY6vhmfujgahjAuCVuX7B37IlxAMdUA3vydXJxxDqYzudtYwCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:05:36.879293Z","bundle_sha256":"ee4ad92404c2be2bb4f2af8659d8a2bab44b2305631fdcd8546054307bacd7c6"}}