{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DXQ66IBRHCX5W6R2WXOI3IH5F2","short_pith_number":"pith:DXQ66IBR","canonical_record":{"source":{"id":"0909.4648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-25T09:17:25Z","cross_cats_sorted":[],"title_canon_sha256":"577fc9ba408347433ce08fe6bed246ae8ba49510d4e67fe815a03fde7292f50d","abstract_canon_sha256":"4e11dea24b4be9a45f541dd4f5d5a08e31092fb85c47f89e3df3279efdfb50cf"},"schema_version":"1.0"},"canonical_sha256":"1de1ef203138afdb7a3ab5dc8da0fd2eb7cb2bc187e86f4408b46a85bca822c0","source":{"kind":"arxiv","id":"0909.4648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4648","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4648v1","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4648","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"DXQ66IBRHCX5","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DXQ66IBRHCX5W6R2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DXQ66IBR","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DXQ66IBRHCX5W6R2WXOI3IH5F2","target":"record","payload":{"canonical_record":{"source":{"id":"0909.4648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-25T09:17:25Z","cross_cats_sorted":[],"title_canon_sha256":"577fc9ba408347433ce08fe6bed246ae8ba49510d4e67fe815a03fde7292f50d","abstract_canon_sha256":"4e11dea24b4be9a45f541dd4f5d5a08e31092fb85c47f89e3df3279efdfb50cf"},"schema_version":"1.0"},"canonical_sha256":"1de1ef203138afdb7a3ab5dc8da0fd2eb7cb2bc187e86f4408b46a85bca822c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:50.830848Z","signature_b64":"PxG/mgoyYCCPvkSbZvgg2yP4t8v22SCKdnhbYpnpx7+eRYef8zopmUtM6/OBUU6SWHB5y8zS1PIxMjFVZBkYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1de1ef203138afdb7a3ab5dc8da0fd2eb7cb2bc187e86f4408b46a85bca822c0","last_reissued_at":"2026-05-18T04:38:50.830213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:50.830213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.4648","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":"2026-05-18T04:38:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J7rfCFWKxxVr3LpVJKX3j+LYDGjbJSXqQOVRlZemEnREaF0VYxHeSoEW9YvNRUIifsosOHAuM07STgpdBGwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:53:20.783461Z"},"content_sha256":"3d39133e7005023281f6184b46268da96a59a739066ce2ba1264e73d2eaba8ff","schema_version":"1.0","event_id":"sha256:3d39133e7005023281f6184b46268da96a59a739066ce2ba1264e73d2eaba8ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DXQ66IBRHCX5W6R2WXOI3IH5F2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Arnd R\\\"osch, Dirk A. Lorenz","submitted_at":"2009-09-25T09:17:25Z","abstract_excerpt":"We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this results we show, that if the solution of the unconstrained problem has no active constraints, the same holds for the Tikhonov-regularized solution if the regularization parameter is small enough and a certain source condition is fulfilled."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4648","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":"2026-05-18T04:38:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeZds1//YVcueWQORSK86nHIzHlgH0GZOjU9mCIquDHiTKGT85hOHIlk4/Erj7nzMKR3J30Gw4CP/cX+6RtGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:53:20.783811Z"},"content_sha256":"c186d7d0e78b94123b6182b02b45b8be632b1b275305d01f8a7d751a52277124","schema_version":"1.0","event_id":"sha256:c186d7d0e78b94123b6182b02b45b8be632b1b275305d01f8a7d751a52277124"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/bundle.json","state_url":"https://pith.science/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/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":"2026-05-20T15:53:20Z","links":{"resolver":"https://pith.science/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2","bundle":"https://pith.science/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/bundle.json","state":"https://pith.science/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXQ66IBRHCX5W6R2WXOI3IH5F2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DXQ66IBRHCX5W6R2WXOI3IH5F2","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":"4e11dea24b4be9a45f541dd4f5d5a08e31092fb85c47f89e3df3279efdfb50cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-25T09:17:25Z","title_canon_sha256":"577fc9ba408347433ce08fe6bed246ae8ba49510d4e67fe815a03fde7292f50d"},"schema_version":"1.0","source":{"id":"0909.4648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4648","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4648v1","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4648","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"DXQ66IBRHCX5","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DXQ66IBRHCX5W6R2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DXQ66IBR","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:c186d7d0e78b94123b6182b02b45b8be632b1b275305d01f8a7d751a52277124","target":"graph","created_at":"2026-05-18T04:38:50Z","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":"We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this results we show, that if the solution of the unconstrained problem has no active constraints, the same holds for the Tikhonov-regularized solution if the regularization parameter is small enough and a certain source condition is fulfilled.","authors_text":"Arnd R\\\"osch, Dirk A. Lorenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-25T09:17:25Z","title":"Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4648","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":"sha256:3d39133e7005023281f6184b46268da96a59a739066ce2ba1264e73d2eaba8ff","target":"record","created_at":"2026-05-18T04:38:50Z","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":"4e11dea24b4be9a45f541dd4f5d5a08e31092fb85c47f89e3df3279efdfb50cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-25T09:17:25Z","title_canon_sha256":"577fc9ba408347433ce08fe6bed246ae8ba49510d4e67fe815a03fde7292f50d"},"schema_version":"1.0","source":{"id":"0909.4648","kind":"arxiv","version":1}},"canonical_sha256":"1de1ef203138afdb7a3ab5dc8da0fd2eb7cb2bc187e86f4408b46a85bca822c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1de1ef203138afdb7a3ab5dc8da0fd2eb7cb2bc187e86f4408b46a85bca822c0","first_computed_at":"2026-05-18T04:38:50.830213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:50.830213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PxG/mgoyYCCPvkSbZvgg2yP4t8v22SCKdnhbYpnpx7+eRYef8zopmUtM6/OBUU6SWHB5y8zS1PIxMjFVZBkYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:50.830848Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d39133e7005023281f6184b46268da96a59a739066ce2ba1264e73d2eaba8ff","sha256:c186d7d0e78b94123b6182b02b45b8be632b1b275305d01f8a7d751a52277124"],"state_sha256":"5d8a6a17e27371facda2076b19f64bee2048c7a27954e966832acf9772dddc19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kg28quoRy6EA3VNKNJFqNxp9k/9rmaD9J2PuUzBDH7g4rnnqPuCHmK5lUieg/gGKH0FM3agjMTas/FxA6gG0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:53:20.785849Z","bundle_sha256":"d739736f7798dd00f89903e15001919cb8192d5da4c38c18cd944af2b0b16de4"}}