{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MAKLBZUUSKW7O2E2JBUB5B33EO","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":"743275cba6ed9c01b3ae22b0f8d286317e164fcaa58166beece940ce38afd0e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-15T07:27:03Z","title_canon_sha256":"297d1b932240c7d469c77ab8647c836f2c0f5bbaea59b1f9be98f1299ec44291"},"schema_version":"1.0","source":{"id":"1404.3834","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3834","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3834v3","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3834","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"pith_short_12","alias_value":"MAKLBZUUSKW7","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MAKLBZUUSKW7O2E2","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MAKLBZUU","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:404c929aedd825d821e9ff9c800573b15dc01d0eb128b71cd54f1a9a53c1e3ed","target":"graph","created_at":"2026-05-18T02:52:14Z","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 study filter based regularization methods for linear ill-posed problems between Hilbert spaces. We derive optimal order conditions under a-priori choice rules for the regularization parameter. Such analysis is applied to the fractional Tikhonov method and the weighted Tikhonov method recently investigated in [9] and [8], respectively. These variants of the classical Tikhonov method can be viewed as classes of methods depending on a further parameter, controlling the smoothness of the computed solution. From our previous analysis, we derive sufficient conditions on such parameter in order to","authors_text":"Davide Bianchi, Marco Donatelli, Stefano Serra-Capizzano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-15T07:27:03Z","title":"Optimal order conditions for filter based regularization methods, with applications to variants of the Tikhonov method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3834","kind":"arxiv","version":3},"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:c95e1325c0241cc1f1819d04be5e27dbab3cb98dc2dd58420063ef7cf4189b80","target":"record","created_at":"2026-05-18T02:52:14Z","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":"743275cba6ed9c01b3ae22b0f8d286317e164fcaa58166beece940ce38afd0e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-15T07:27:03Z","title_canon_sha256":"297d1b932240c7d469c77ab8647c836f2c0f5bbaea59b1f9be98f1299ec44291"},"schema_version":"1.0","source":{"id":"1404.3834","kind":"arxiv","version":3}},"canonical_sha256":"6014b0e69492adf7689a48681e877b2395b131206c6890ab145222efaeb12b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6014b0e69492adf7689a48681e877b2395b131206c6890ab145222efaeb12b8d","first_computed_at":"2026-05-18T02:52:14.859940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:14.859940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JCvN+sTl6FcZ8LC2ONVu+qQ0FOKRrL/Vw5ynyfM2CVZ1W27yvk9/Z7jXNkTioet6MwI2Y3pVWL1aOlx0a2ZZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:14.860615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3834","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c95e1325c0241cc1f1819d04be5e27dbab3cb98dc2dd58420063ef7cf4189b80","sha256:404c929aedd825d821e9ff9c800573b15dc01d0eb128b71cd54f1a9a53c1e3ed"],"state_sha256":"57b4312372c943726653344bcf32310ebb7cbc15793d3f2ba615fb9ce26cf3fa"}