{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T6IJRZ7PCE5DXWDSZXFBEF3DTT","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":"a13f23726a9138f23dad0a4e4f008d7b5439b0d8dbc0ac26c991e620158a54e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-26T04:47:09Z","title_canon_sha256":"a28dd0b2c1176dcc368fe2a8966bfd7631e296a8d3cab33355d8bc9a71ee7093"},"schema_version":"1.0","source":{"id":"1709.09539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09539","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09539v1","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09539","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"pith_short_12","alias_value":"T6IJRZ7PCE5D","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T6IJRZ7PCE5DXWDS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T6IJRZ7P","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:5fc52fa93ab429c5b78ec0bf6f5051ebd4885ee617f45acb9af9c52346a64b8e","target":"graph","created_at":"2026-05-18T00:34:11Z","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":"Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized $L^1$-norm does not have a decoupled form when the standard piecewise linear finite element is employed to discretize the continuous problem. A common approach to overcome this difficulty is employing a nodal quadrature formula to approximately discretize the $L^1$-norm. It is inevitable that this technique will incur an additional error. Different from the ","authors_text":"Bo Chen, Bo Yu, Xiaoliang Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-26T04:47:09Z","title":"Error Estimates for Sparse Optimal Control Problems by Piecewise Linear Finite Element Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09539","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:c8a0a7805539af6488dc039e6bd600477bc8808467e26f8d99c6082804cb2416","target":"record","created_at":"2026-05-18T00:34:11Z","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":"a13f23726a9138f23dad0a4e4f008d7b5439b0d8dbc0ac26c991e620158a54e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-26T04:47:09Z","title_canon_sha256":"a28dd0b2c1176dcc368fe2a8966bfd7631e296a8d3cab33355d8bc9a71ee7093"},"schema_version":"1.0","source":{"id":"1709.09539","kind":"arxiv","version":1}},"canonical_sha256":"9f9098e7ef113a3bd872cdca1217639cce9cb830a6f1f1cb63e8894c8f9b2ef5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f9098e7ef113a3bd872cdca1217639cce9cb830a6f1f1cb63e8894c8f9b2ef5","first_computed_at":"2026-05-18T00:34:11.391131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:11.391131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXJspEYbP4l40qhnmInY2d0dVwzbj+SqCsj7YLxyPlJMkdhYP3F1emcaHmdfmtrsEzI44FVOdc52KEHm+XonBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:11.391800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8a0a7805539af6488dc039e6bd600477bc8808467e26f8d99c6082804cb2416","sha256:5fc52fa93ab429c5b78ec0bf6f5051ebd4885ee617f45acb9af9c52346a64b8e"],"state_sha256":"cc138c4d28abd21946b38a5a9e3685d13d9198b26d372ab5b01b9fc143a3c56b"}