{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BC5PUHOKTS7KVGC4HTFMIWEWBU","short_pith_number":"pith:BC5PUHOK","schema_version":"1.0","canonical_sha256":"08bafa1dca9cbeaa985c3ccac458960d0ddfbd2da2ae99ae9f25122b5eb234bd","source":{"kind":"arxiv","id":"1907.00349","version":1},"attestation_state":"computed","paper":{"title":"A multiscale reduced basis method for Schr\\\"{o}dinger equation with multiscale and random potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dingjiong Ma, Jingrun Chen, Zhiwen Zhang","submitted_at":"2019-06-30T10:04:30Z","abstract_excerpt":"The semiclassical Schr\\\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical space and the random space, which poses severe challenges for numerical methods. In this paper, we propose a multiscale reduced basis method, where we construct multiscale reduced basis functions using an optimization method and the proper orthogonal decomposition method in the physical space and employ the quasi-Monte Carlo method in the random"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.00349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T10:04:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b4629d8817d4d22a7434b7c06d5687c21ca37212676d1f89b940d7218a391518","abstract_canon_sha256":"b989992ea129ee27030b3714b8bd6c35cee153fc3cc534bd9ea3bf5c96992755"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:52.067677Z","signature_b64":"awOQBSvjY4c6tXzzvUphyi4OIDnl5R3dgnpTprSNrbiLQbMhtqPwmn8ogJEvfUpFdRf/eUoJLRGczTYZXOF1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08bafa1dca9cbeaa985c3ccac458960d0ddfbd2da2ae99ae9f25122b5eb234bd","last_reissued_at":"2026-05-17T23:41:52.067070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:52.067070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A multiscale reduced basis method for Schr\\\"{o}dinger equation with multiscale and random potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dingjiong Ma, Jingrun Chen, Zhiwen Zhang","submitted_at":"2019-06-30T10:04:30Z","abstract_excerpt":"The semiclassical Schr\\\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical space and the random space, which poses severe challenges for numerical methods. In this paper, we propose a multiscale reduced basis method, where we construct multiscale reduced basis functions using an optimization method and the proper orthogonal decomposition method in the physical space and employ the quasi-Monte Carlo method in the random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00349","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.00349","created_at":"2026-05-17T23:41:52.067155+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.00349v1","created_at":"2026-05-17T23:41:52.067155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00349","created_at":"2026-05-17T23:41:52.067155+00:00"},{"alias_kind":"pith_short_12","alias_value":"BC5PUHOKTS7K","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BC5PUHOKTS7KVGC4","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BC5PUHOK","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU","json":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU.json","graph_json":"https://pith.science/api/pith-number/BC5PUHOKTS7KVGC4HTFMIWEWBU/graph.json","events_json":"https://pith.science/api/pith-number/BC5PUHOKTS7KVGC4HTFMIWEWBU/events.json","paper":"https://pith.science/paper/BC5PUHOK"},"agent_actions":{"view_html":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU","download_json":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU.json","view_paper":"https://pith.science/paper/BC5PUHOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.00349&json=true","fetch_graph":"https://pith.science/api/pith-number/BC5PUHOKTS7KVGC4HTFMIWEWBU/graph.json","fetch_events":"https://pith.science/api/pith-number/BC5PUHOKTS7KVGC4HTFMIWEWBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU/action/storage_attestation","attest_author":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU/action/author_attestation","sign_citation":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU/action/citation_signature","submit_replication":"https://pith.science/pith/BC5PUHOKTS7KVGC4HTFMIWEWBU/action/replication_record"}},"created_at":"2026-05-17T23:41:52.067155+00:00","updated_at":"2026-05-17T23:41:52.067155+00:00"}