{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ALWSVJXISH45Z4SXBVIBCVGC35","short_pith_number":"pith:ALWSVJXI","schema_version":"1.0","canonical_sha256":"02ed2aa6e891f9dcf2570d501154c2df7c8c008119d0eafceddce7c018d4638c","source":{"kind":"arxiv","id":"2201.02687","version":1},"attestation_state":"computed","paper":{"title":"A Direct Parallel-in-Time Quasi-Boundary Value Method for Inverse Space-Dependent Source Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jun Liu, Xiang-Sheng Wang, Yi Jiang","submitted_at":"2022-01-07T21:48:10Z","abstract_excerpt":"Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been proposed and analyzed as an effective way for regularizing such inverse source problems, which was shown to achieve an optimal order convergence rate under suitable assumptions. However, fast direct or iterative solvers for the resulting all-at-once large-scale linear systems have been rarely studied in the literature. In this work, we first proposed and analyzed a modified quasi-bounda"},"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":"2201.02687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-01-07T21:48:10Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"276d984d8f4979222acb346b00993a2237a5d331bf80ffdfc19853aa4f6e922a","abstract_canon_sha256":"43111f2b7d45c98c54551ff83232cf04e4357bd42acd73c6555e481b356feccd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:46:47.162722Z","signature_b64":"SiIIUT6x6tCHouAvr01PpuP0w7O2H7NkkE1vJCREea3VoDpw5Uj5RR8CtGm+Npa9OUPNU+1O6P0uTbURBnkDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ed2aa6e891f9dcf2570d501154c2df7c8c008119d0eafceddce7c018d4638c","last_reissued_at":"2026-07-05T03:46:47.162366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:46:47.162366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Direct Parallel-in-Time Quasi-Boundary Value Method for Inverse Space-Dependent Source Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jun Liu, Xiang-Sheng Wang, Yi Jiang","submitted_at":"2022-01-07T21:48:10Z","abstract_excerpt":"Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been proposed and analyzed as an effective way for regularizing such inverse source problems, which was shown to achieve an optimal order convergence rate under suitable assumptions. However, fast direct or iterative solvers for the resulting all-at-once large-scale linear systems have been rarely studied in the literature. In this work, we first proposed and analyzed a modified quasi-bounda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02687","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.02687/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2201.02687","created_at":"2026-07-05T03:46:47.162429+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.02687v1","created_at":"2026-07-05T03:46:47.162429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02687","created_at":"2026-07-05T03:46:47.162429+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALWSVJXISH45","created_at":"2026-07-05T03:46:47.162429+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALWSVJXISH45Z4SX","created_at":"2026-07-05T03:46:47.162429+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALWSVJXI","created_at":"2026-07-05T03:46:47.162429+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/ALWSVJXISH45Z4SXBVIBCVGC35","json":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35.json","graph_json":"https://pith.science/api/pith-number/ALWSVJXISH45Z4SXBVIBCVGC35/graph.json","events_json":"https://pith.science/api/pith-number/ALWSVJXISH45Z4SXBVIBCVGC35/events.json","paper":"https://pith.science/paper/ALWSVJXI"},"agent_actions":{"view_html":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35","download_json":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35.json","view_paper":"https://pith.science/paper/ALWSVJXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.02687&json=true","fetch_graph":"https://pith.science/api/pith-number/ALWSVJXISH45Z4SXBVIBCVGC35/graph.json","fetch_events":"https://pith.science/api/pith-number/ALWSVJXISH45Z4SXBVIBCVGC35/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35/action/storage_attestation","attest_author":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35/action/author_attestation","sign_citation":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35/action/citation_signature","submit_replication":"https://pith.science/pith/ALWSVJXISH45Z4SXBVIBCVGC35/action/replication_record"}},"created_at":"2026-07-05T03:46:47.162429+00:00","updated_at":"2026-07-05T03:46:47.162429+00:00"}