{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YDSG6KM4LNZSUMRLUWOA5UULZS","short_pith_number":"pith:YDSG6KM4","canonical_record":{"source":{"id":"2410.14106","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-18T01:14:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9cda10784e5fae51184e86996339cff3fefd7dca104b3a0ca36138c748704f1e","abstract_canon_sha256":"c8fea3595e5475bcf5340b66e79c62c7c311c87746d87fb3165408c96e374716"},"schema_version":"1.0"},"canonical_sha256":"c0e46f299c5b732a322ba59c0ed28bcca3737872fe9b618220aff24c91b2f393","source":{"kind":"arxiv","id":"2410.14106","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.14106","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"arxiv_version","alias_value":"2410.14106v2","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.14106","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_12","alias_value":"YDSG6KM4LNZS","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_16","alias_value":"YDSG6KM4LNZSUMRL","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_8","alias_value":"YDSG6KM4","created_at":"2026-07-05T11:11:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YDSG6KM4LNZSUMRLUWOA5UULZS","target":"record","payload":{"canonical_record":{"source":{"id":"2410.14106","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-18T01:14:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9cda10784e5fae51184e86996339cff3fefd7dca104b3a0ca36138c748704f1e","abstract_canon_sha256":"c8fea3595e5475bcf5340b66e79c62c7c311c87746d87fb3165408c96e374716"},"schema_version":"1.0"},"canonical_sha256":"c0e46f299c5b732a322ba59c0ed28bcca3737872fe9b618220aff24c91b2f393","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:36.128182Z","signature_b64":"i+oE7QgZQ426d5Ls17DpO79scdYj9o4WgmrNb+wpFW0OWquLxFLdhVPuFIBjdxJgI6NYO2ixB7Ud7zjd9IMmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0e46f299c5b732a322ba59c0ed28bcca3737872fe9b618220aff24c91b2f393","last_reissued_at":"2026-07-05T11:11:36.127633Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:36.127633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.14106","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":"2026-07-05T11:11:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQ4g6LX6B2cuxwnt1SjINvFPP0qim7OJLZyos0DQpxkbebvnGnToKtNh3o/xP+Fx1K8YFgmA5td+KdOf31gDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T23:07:00.965134Z"},"content_sha256":"a212a343b1b834b580fbb8222f1ed150e3f624085b9b0a1b35d0a8ae273457b9","schema_version":"1.0","event_id":"sha256:a212a343b1b834b580fbb8222f1ed150e3f624085b9b0a1b35d0a8ae273457b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YDSG6KM4LNZSUMRLUWOA5UULZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Convergence Analysis of Inverse Potential Problem","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bangti Jin, Qimeng Quan, Wenlong Zhang","submitted_at":"2024-10-18T01:14:32Z","abstract_excerpt":"In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a least squares formulation with an $H^1(\\Omega)$ penalty on the potential in order to obtain a numerical reconstruction, and the Galerkin finite element method for the spatial discretization. Under mild regularity assumptions on the problem data, we provide a stochastic $L^2(\\Omega)$ convergence analysis on the regularized solution and the finite element approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.14106","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.14106/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oMr76/VFitSetZJiOxtzaZ/wa6724gh22y6ssIdayFqrdplYHSsS55LdVcb2c6UkUCt/c2D7OpGQdh2nyRZNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T23:07:00.965704Z"},"content_sha256":"a06db0410bc58a76bb4512b04ae342736a18635789f398d1b44f864cc631c0b6","schema_version":"1.0","event_id":"sha256:a06db0410bc58a76bb4512b04ae342736a18635789f398d1b44f864cc631c0b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/bundle.json","state_url":"https://pith.science/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/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":"2026-08-22T23:07:00Z","links":{"resolver":"https://pith.science/pith/YDSG6KM4LNZSUMRLUWOA5UULZS","bundle":"https://pith.science/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/bundle.json","state":"https://pith.science/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDSG6KM4LNZSUMRLUWOA5UULZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YDSG6KM4LNZSUMRLUWOA5UULZS","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":"c8fea3595e5475bcf5340b66e79c62c7c311c87746d87fb3165408c96e374716","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-18T01:14:32Z","title_canon_sha256":"9cda10784e5fae51184e86996339cff3fefd7dca104b3a0ca36138c748704f1e"},"schema_version":"1.0","source":{"id":"2410.14106","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.14106","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"arxiv_version","alias_value":"2410.14106v2","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.14106","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_12","alias_value":"YDSG6KM4LNZS","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_16","alias_value":"YDSG6KM4LNZSUMRL","created_at":"2026-07-05T11:11:36Z"},{"alias_kind":"pith_short_8","alias_value":"YDSG6KM4","created_at":"2026-07-05T11:11:36Z"}],"graph_snapshots":[{"event_id":"sha256:a06db0410bc58a76bb4512b04ae342736a18635789f398d1b44f864cc631c0b6","target":"graph","created_at":"2026-07-05T11:11:36Z","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/2410.14106/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a least squares formulation with an $H^1(\\Omega)$ penalty on the potential in order to obtain a numerical reconstruction, and the Galerkin finite element method for the spatial discretization. Under mild regularity assumptions on the problem data, we provide a stochastic $L^2(\\Omega)$ convergence analysis on the regularized solution and the finite element approx","authors_text":"Bangti Jin, Qimeng Quan, Wenlong Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-18T01:14:32Z","title":"Stochastic Convergence Analysis of Inverse Potential Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.14106","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:a212a343b1b834b580fbb8222f1ed150e3f624085b9b0a1b35d0a8ae273457b9","target":"record","created_at":"2026-07-05T11:11:36Z","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":"c8fea3595e5475bcf5340b66e79c62c7c311c87746d87fb3165408c96e374716","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-18T01:14:32Z","title_canon_sha256":"9cda10784e5fae51184e86996339cff3fefd7dca104b3a0ca36138c748704f1e"},"schema_version":"1.0","source":{"id":"2410.14106","kind":"arxiv","version":2}},"canonical_sha256":"c0e46f299c5b732a322ba59c0ed28bcca3737872fe9b618220aff24c91b2f393","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0e46f299c5b732a322ba59c0ed28bcca3737872fe9b618220aff24c91b2f393","first_computed_at":"2026-07-05T11:11:36.127633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:36.127633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+oE7QgZQ426d5Ls17DpO79scdYj9o4WgmrNb+wpFW0OWquLxFLdhVPuFIBjdxJgI6NYO2ixB7Ud7zjd9IMmBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:36.128182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.14106","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a212a343b1b834b580fbb8222f1ed150e3f624085b9b0a1b35d0a8ae273457b9","sha256:a06db0410bc58a76bb4512b04ae342736a18635789f398d1b44f864cc631c0b6"],"state_sha256":"227e7ebd13769c5e0b1e696274734bd3d2d380d9e90993c598c3b969214257d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xuVvuCTAKGRCeOldTYpUBhULceh1HyMjVCxqlvGY2CT65WHopRAXLCu+pIYiCPu08m2/vNLOrQmUFU3xiMGcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T23:07:00.969536Z","bundle_sha256":"a68b1fd0d833a20ba03f8ca7dea4d93b744af91fcf63797e5348f7e88943c1c3"}}