{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OTI7CMGZJPFZ422ZQUCORPWRRO","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":"92fb275a01e71cd809d017e252ca2b7dc3ffded3e1804f5bbf4d278c375f7f6a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-03T14:18:42Z","title_canon_sha256":"f1e78fd1e8013235e4d5a0b0aa0807016509a7ea20dbf81391f95c2dd13133d5"},"schema_version":"1.0","source":{"id":"1805.01320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01320","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01320v1","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01320","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"OTI7CMGZJPFZ","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"OTI7CMGZJPFZ422Z","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"OTI7CMGZ","created_at":"2026-06-04T19:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:3c2b4c4103216afad0e14180a590f90b62ae374c11f986e34b417feac121057a","target":"graph","created_at":"2026-06-04T19:11:51Z","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/1805.01320/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The authors study Tikhonov regularization of linear ill-posed problems with a general convex penalty defined on a Banach space. It is well known that the error analysis requires smoothness assumptions. Here such assumptions are given in form of inequalities involving only the family of noise-free minimizers along the regularization parameter and the (unknown) penalty-minimizing solution. These inequalities control, respectively, the defect of the penalty, or likewise, the defect of the whole Tikhonov functional. The main results provide error bounds for a Bregman distance, which split into two","authors_text":"Bernd Hofmann, Peter Math\\'e, Stefan Kindermann","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-03T14:18:42Z","title":"Penalty-based smoothness conditions in convex variational regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01320","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":"sha256:0e445df5009e92f8051d358bde0920b04429fc2eb5e6493bab58f38b6b3bc6ef","target":"record","created_at":"2026-06-04T19:11:51Z","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":"92fb275a01e71cd809d017e252ca2b7dc3ffded3e1804f5bbf4d278c375f7f6a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-03T14:18:42Z","title_canon_sha256":"f1e78fd1e8013235e4d5a0b0aa0807016509a7ea20dbf81391f95c2dd13133d5"},"schema_version":"1.0","source":{"id":"1805.01320","kind":"arxiv","version":1}},"canonical_sha256":"74d1f130d94bcb9e6b598504e8bed18b86625d2863d14b1fdf216621b0a870ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74d1f130d94bcb9e6b598504e8bed18b86625d2863d14b1fdf216621b0a870ab","first_computed_at":"2026-06-04T19:11:51.444980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:51.444980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ELfrMSoCGAOf6edA/lFNzdKqo2MyCxwmz8wNwT2kyUGrQOJ6SI+5UJmVl/o02jEYv587PkmPr+euS65pTjNhCA==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:51.445418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e445df5009e92f8051d358bde0920b04429fc2eb5e6493bab58f38b6b3bc6ef","sha256:3c2b4c4103216afad0e14180a590f90b62ae374c11f986e34b417feac121057a"],"state_sha256":"4feaf9f073d25294159d9eae2e0c1456e2dbd7fd2d0134b0678bab00f9276944"}