{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VUPDT2DY4EXLD7CI7UF3QETVN2","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":"85a6837746a0a885707f777e5fad11e6e07c6f2a552208697e5f710848627ae5","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-09T17:22:24Z","title_canon_sha256":"7fb2c06f9119d7c2754dfcca17cfbf99074408281da5e54dc492561929ccda54"},"schema_version":"1.0","source":{"id":"2203.04899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.04899","created_at":"2026-07-05T05:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"2203.04899v2","created_at":"2026-07-05T05:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.04899","created_at":"2026-07-05T05:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"VUPDT2DY4EXL","created_at":"2026-07-05T05:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"VUPDT2DY4EXLD7CI","created_at":"2026-07-05T05:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"VUPDT2DY","created_at":"2026-07-05T05:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:57598dea175963b0aa9c98f39b9706aa29b06dee5783abb986316c1cc61848ee","target":"graph","created_at":"2026-07-05T05:26:39Z","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/2203.04899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very mild conditions on the problem data. Then we provide an error analysis of a standard reconstruction scheme based on the standard output least-squares formulation with Tikhonov regularization (by an $H^1$-seminorm penalty), which is then discretized by the Galerkin finite element method with continuous piecewise linear finite elements in space (and also backwar","authors_text":"Bangti Jin, Qimeng Quan, Xiliang Lu, Zhi Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-09T17:22:24Z","title":"Convergence Rate Analysis of Galerkin Approximation of Inverse Potential Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04899","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":"sha256:251ca5d629b8ba8c63d5a1a337b67871048fead0f5d9955c574e0327aeb83a72","target":"record","created_at":"2026-07-05T05:26:39Z","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":"85a6837746a0a885707f777e5fad11e6e07c6f2a552208697e5f710848627ae5","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-09T17:22:24Z","title_canon_sha256":"7fb2c06f9119d7c2754dfcca17cfbf99074408281da5e54dc492561929ccda54"},"schema_version":"1.0","source":{"id":"2203.04899","kind":"arxiv","version":2}},"canonical_sha256":"ad1e39e878e12eb1fc48fd0bb812756ead8b7becd0eb2e087170cfc1b4d32bc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad1e39e878e12eb1fc48fd0bb812756ead8b7becd0eb2e087170cfc1b4d32bc2","first_computed_at":"2026-07-05T05:26:39.124246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:26:39.124246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BdxSW5Ram2+45LTNVj6boFArNGq4k9/zVlbu0hA+GsN3smkLuRX3N6cQ6OuxQhwXVDJuvxOW56N2MXERr8uiCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:26:39.124744Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.04899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:251ca5d629b8ba8c63d5a1a337b67871048fead0f5d9955c574e0327aeb83a72","sha256:57598dea175963b0aa9c98f39b9706aa29b06dee5783abb986316c1cc61848ee"],"state_sha256":"7b7e70e30b7278be0463eb173958f490b99caa20d7c72e50259235290c49df6b"}