{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GALL4DZMLG5EBU24B6LGM7BDGO","short_pith_number":"pith:GALL4DZM","canonical_record":{"source":{"id":"1209.3903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-18T10:32:57Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6c4c2458fda0821571c7a85dab1a768420c943fcc262c18a9e1d3ec6b7ec106d","abstract_canon_sha256":"bbad885460a38b597cfdcd9061e22a1d3c3307def4744ec069bc8e436474f002"},"schema_version":"1.0"},"canonical_sha256":"3016be0f2c59ba40d35c0f96667c23338fb63e2a0a252fd15857efc651856e22","source":{"kind":"arxiv","id":"1209.3903","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3903","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3903v2","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3903","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"GALL4DZMLG5E","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GALL4DZMLG5EBU24","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GALL4DZM","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GALL4DZMLG5EBU24B6LGM7BDGO","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-18T10:32:57Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6c4c2458fda0821571c7a85dab1a768420c943fcc262c18a9e1d3ec6b7ec106d","abstract_canon_sha256":"bbad885460a38b597cfdcd9061e22a1d3c3307def4744ec069bc8e436474f002"},"schema_version":"1.0"},"canonical_sha256":"3016be0f2c59ba40d35c0f96667c23338fb63e2a0a252fd15857efc651856e22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:14.002050Z","signature_b64":"BYC9lNqUTQT/4UIYlTLZZc5yCszqf1V5J6p02K6z3j2zTVOZbOIefP1aE7wHOIJ39fA8Tgyr7GI8VnovSuegBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3016be0f2c59ba40d35c0f96667c23338fb63e2a0a252fd15857efc651856e22","last_reissued_at":"2026-05-18T03:04:14.001663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:14.001663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3903","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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/u5D6nP+6RQEXcKAw/NzE8lyhZhG8W+4Go/IOpRXK2C/UMXSgsSUCJg9NpI8hxXoAzRw/E8onWQEycq/1IciDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:18:03.285979Z"},"content_sha256":"5be4a59110581aeba8208279a75c2f6ed3e8317133edbd21398ab4fbf8d9ebb6","schema_version":"1.0","event_id":"sha256:5be4a59110581aeba8208279a75c2f6ed3e8317133edbd21398ab4fbf8d9ebb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GALL4DZMLG5EBU24B6LGM7BDGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"R\\'emi Carles (I3M)","submitted_at":"2012-09-18T10:32:57Z","abstract_excerpt":"We prove an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible Euler-Poisson equation is smooth, the error between the numerical solution and the exact solution is controlled in Sobolev spaces, in a suitable phase/amplitude representation. As a corollary, we infer the numerical convergence of the quadratic observables with a time step independent of the Planck constant. A similar result is established for the nonlinear S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3903","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":""},"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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxqWxwL8fcs/0rYxKUQofxEC5wYMsvineLSGDakkSZ9Y1lwhwDvV/mpCX+jDG4AUlSO4iDJU3xyl2A69TU+TBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:18:03.286893Z"},"content_sha256":"9a36c4555f4a1a61bc68c68f90566c4a82344479af33c42b903ec4ec5dc54a9e","schema_version":"1.0","event_id":"sha256:9a36c4555f4a1a61bc68c68f90566c4a82344479af33c42b903ec4ec5dc54a9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GALL4DZMLG5EBU24B6LGM7BDGO/bundle.json","state_url":"https://pith.science/pith/GALL4DZMLG5EBU24B6LGM7BDGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GALL4DZMLG5EBU24B6LGM7BDGO/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":"2026-08-04T15:18:03Z","links":{"resolver":"https://pith.science/pith/GALL4DZMLG5EBU24B6LGM7BDGO","bundle":"https://pith.science/pith/GALL4DZMLG5EBU24B6LGM7BDGO/bundle.json","state":"https://pith.science/pith/GALL4DZMLG5EBU24B6LGM7BDGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GALL4DZMLG5EBU24B6LGM7BDGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GALL4DZMLG5EBU24B6LGM7BDGO","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":"bbad885460a38b597cfdcd9061e22a1d3c3307def4744ec069bc8e436474f002","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-18T10:32:57Z","title_canon_sha256":"6c4c2458fda0821571c7a85dab1a768420c943fcc262c18a9e1d3ec6b7ec106d"},"schema_version":"1.0","source":{"id":"1209.3903","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3903","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3903v2","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3903","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"GALL4DZMLG5E","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GALL4DZMLG5EBU24","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GALL4DZM","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:9a36c4555f4a1a61bc68c68f90566c4a82344479af33c42b903ec4ec5dc54a9e","target":"graph","created_at":"2026-05-18T03:04:14Z","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 an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible Euler-Poisson equation is smooth, the error between the numerical solution and the exact solution is controlled in Sobolev spaces, in a suitable phase/amplitude representation. As a corollary, we infer the numerical convergence of the quadratic observables with a time step independent of the Planck constant. A similar result is established for the nonlinear S","authors_text":"R\\'emi Carles (I3M)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-18T10:32:57Z","title":"On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3903","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":"sha256:5be4a59110581aeba8208279a75c2f6ed3e8317133edbd21398ab4fbf8d9ebb6","target":"record","created_at":"2026-05-18T03:04:14Z","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":"bbad885460a38b597cfdcd9061e22a1d3c3307def4744ec069bc8e436474f002","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-18T10:32:57Z","title_canon_sha256":"6c4c2458fda0821571c7a85dab1a768420c943fcc262c18a9e1d3ec6b7ec106d"},"schema_version":"1.0","source":{"id":"1209.3903","kind":"arxiv","version":2}},"canonical_sha256":"3016be0f2c59ba40d35c0f96667c23338fb63e2a0a252fd15857efc651856e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3016be0f2c59ba40d35c0f96667c23338fb63e2a0a252fd15857efc651856e22","first_computed_at":"2026-05-18T03:04:14.001663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.001663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BYC9lNqUTQT/4UIYlTLZZc5yCszqf1V5J6p02K6z3j2zTVOZbOIefP1aE7wHOIJ39fA8Tgyr7GI8VnovSuegBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.002050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3903","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5be4a59110581aeba8208279a75c2f6ed3e8317133edbd21398ab4fbf8d9ebb6","sha256:9a36c4555f4a1a61bc68c68f90566c4a82344479af33c42b903ec4ec5dc54a9e"],"state_sha256":"f129e5506544aac4a16e7871b93a6333378b66ca2bca4756e6eac6bc56dfdd85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmPSCwhGs/XD+W0Eyef63FVDqP2HAeZlbg8/b28Zm9a2/28KAS82v868WoTJbB4DFUe43ivXmWTAOibgRnLjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:18:03.292316Z","bundle_sha256":"ff0a2b31899177c4cdd5ef1c538ab1b3438ac2e6669b3da3bccafb7a97e6363f"}}