{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ECANLKUXFVBQDQQI6FQ6OQGPOM","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":"5ef3366ee0571bd881220903397b7a8bab152acfd28e6d84e35a422c80c83bc7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-09T17:20:01Z","title_canon_sha256":"28b6b52e44809d7766d5b17373ea0fad3570f1eff30986acd020d1c4d30575f7"},"schema_version":"1.0","source":{"id":"1503.02564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02564","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02564v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02564","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"ECANLKUXFVBQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ECANLKUXFVBQDQQI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ECANLKUX","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:37e76cdd29b0f0f3f3807fc7abf6abdba7ca4a5ef074b2ef22981d49032affe1","target":"graph","created_at":"2026-05-18T02:25:19Z","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":"In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{\\\"o}dinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schr{\\\"o}dinger equation with time independent linear potential, which is robust and scalable up to 500 subdo-mains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time dependent linear potential or the non-linear potential, we use a preprocessed linear operator for the zero potential case as preconditioner which lead to a preconditioned al","authors_text":"C Besse (IMT), F Xing (MDLS, LPP)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-09T17:20:01Z","title":"Schwarz waveform relaxation method for one dimensional Schr{\\\"o}dinger equation with general potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02564","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:b95a1eadb13fcbf58049c6ffc2b50b14a58c5b83c9e2c93f0e6cbeaad4259697","target":"record","created_at":"2026-05-18T02:25:19Z","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":"5ef3366ee0571bd881220903397b7a8bab152acfd28e6d84e35a422c80c83bc7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-09T17:20:01Z","title_canon_sha256":"28b6b52e44809d7766d5b17373ea0fad3570f1eff30986acd020d1c4d30575f7"},"schema_version":"1.0","source":{"id":"1503.02564","kind":"arxiv","version":1}},"canonical_sha256":"2080d5aa972d4301c208f161e740cf733aaf4f1a4a5e5405371a30e69640848c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2080d5aa972d4301c208f161e740cf733aaf4f1a4a5e5405371a30e69640848c","first_computed_at":"2026-05-18T02:25:19.386254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.386254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Y2tScU85BByM3tXZP7CShgjXjCdyNfG6s7PmCz3XXeVQn+C/zCh81bsYqOhvmkM9NZPS1o6IqRV+WjY28jWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.386610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b95a1eadb13fcbf58049c6ffc2b50b14a58c5b83c9e2c93f0e6cbeaad4259697","sha256:37e76cdd29b0f0f3f3807fc7abf6abdba7ca4a5ef074b2ef22981d49032affe1"],"state_sha256":"cebdfe216fc708c690b73ec1e5ae49cad7cbbc74d3ac1c96c3233ebf14543fb5"}