{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T6IJRZ7PCE5DXWDSZXFBEF3DTT","short_pith_number":"pith:T6IJRZ7P","canonical_record":{"source":{"id":"1709.09539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-26T04:47:09Z","cross_cats_sorted":[],"title_canon_sha256":"a28dd0b2c1176dcc368fe2a8966bfd7631e296a8d3cab33355d8bc9a71ee7093","abstract_canon_sha256":"a13f23726a9138f23dad0a4e4f008d7b5439b0d8dbc0ac26c991e620158a54e3"},"schema_version":"1.0"},"canonical_sha256":"9f9098e7ef113a3bd872cdca1217639cce9cb830a6f1f1cb63e8894c8f9b2ef5","source":{"kind":"arxiv","id":"1709.09539","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T6IJRZ7PCE5DXWDSZXFBEF3DTT","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-26T04:47:09Z","cross_cats_sorted":[],"title_canon_sha256":"a28dd0b2c1176dcc368fe2a8966bfd7631e296a8d3cab33355d8bc9a71ee7093","abstract_canon_sha256":"a13f23726a9138f23dad0a4e4f008d7b5439b0d8dbc0ac26c991e620158a54e3"},"schema_version":"1.0"},"canonical_sha256":"9f9098e7ef113a3bd872cdca1217639cce9cb830a6f1f1cb63e8894c8f9b2ef5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:11.391800Z","signature_b64":"eXJspEYbP4l40qhnmInY2d0dVwzbj+SqCsj7YLxyPlJMkdhYP3F1emcaHmdfmtrsEzI44FVOdc52KEHm+XonBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f9098e7ef113a3bd872cdca1217639cce9cb830a6f1f1cb63e8894c8f9b2ef5","last_reissued_at":"2026-05-18T00:34:11.391131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:11.391131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09539","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7snQDBS7BjuKdnmsFLuq9mnhgyr4GY547E8RcMokkw7pDvXKoDyZh2cSEkfBHbv46s/wnHpBt5IkSFBT+w8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T20:38:30.505472Z"},"content_sha256":"c8a0a7805539af6488dc039e6bd600477bc8808467e26f8d99c6082804cb2416","schema_version":"1.0","event_id":"sha256:c8a0a7805539af6488dc039e6bd600477bc8808467e26f8d99c6082804cb2416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T6IJRZ7PCE5DXWDSZXFBEF3DTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error Estimates for Sparse Optimal Control Problems by Piecewise Linear Finite Element Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Chen, Bo Yu, Xiaoliang Song","submitted_at":"2017-09-26T04:47:09Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09539","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"729R1X579KciP2SOFJdxCSLLAsb93evfX5xhEteNo1x6wj4GoD1LtgwDZgKTmo5kzTVzl9/qTAASon6z4RrJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T20:38:30.506176Z"},"content_sha256":"5fc52fa93ab429c5b78ec0bf6f5051ebd4885ee617f45acb9af9c52346a64b8e","schema_version":"1.0","event_id":"sha256:5fc52fa93ab429c5b78ec0bf6f5051ebd4885ee617f45acb9af9c52346a64b8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/bundle.json","state_url":"https://pith.science/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/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":"2026-05-18T20:38:30Z","links":{"resolver":"https://pith.science/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT","bundle":"https://pith.science/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/bundle.json","state":"https://pith.science/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6IJRZ7PCE5DXWDSZXFBEF3DTT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HvT99LPlJx97OifXKwE/G+tlVpQNwjbhKKI/2mftApp7fIkHYh+QOwsFE6ihpN6s8XO13R0u7avadx7pia0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T20:38:30.508241Z","bundle_sha256":"ec080da382b9a56fa776a65b803e3b6ab063ec07fd1161984a9aa1ef1852ccab"}}