{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G37CYGWXOFVTFKET2IRB4ZLLEW","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":"531a76f55afcc326a87a8ec5a3313e4c1bdb74c3d836589ed3fb5aaa5aaae49e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-18T14:01:23Z","title_canon_sha256":"125971bca606d53dee767aaca302dd7eb4afa0552d82aae8a6e389cefc0184e5"},"schema_version":"1.0","source":{"id":"1804.06735","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06735","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06735v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06735","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"G37CYGWXOFVT","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G37CYGWXOFVTFKET","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G37CYGWX","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:9b976dc9141608a26fcd7d86529b4ec6d3590cd450989057dd0f24775eb89cf9","target":"graph","created_at":"2026-05-18T00:07:17Z","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":"In this paper, we establish an initial theory regarding the Second Order Asymptotical Regularization (SOAR) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear inverse problems with applications in the natural sciences, imaging and engineering. We show the regularizing properties of the new method, as well as the corresponding convergence rates. We prove that, under the appropriate source conditions and by using Morozov's conventional discrepancy principle, SOAR exhibits the same power-type convergence rate as the cla","authors_text":"Bernd Hofmann, Ye Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-18T14:01:23Z","title":"On the second order asymptotical regularization of linear ill-posed inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06735","kind":"arxiv","version":2},"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":"sha256:2caeab956d63af2bc9c9dee4bede8b91792cc4ba81850c8d002a6b0502fcedbe","target":"record","created_at":"2026-05-18T00:07:17Z","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":"531a76f55afcc326a87a8ec5a3313e4c1bdb74c3d836589ed3fb5aaa5aaae49e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-18T14:01:23Z","title_canon_sha256":"125971bca606d53dee767aaca302dd7eb4afa0552d82aae8a6e389cefc0184e5"},"schema_version":"1.0","source":{"id":"1804.06735","kind":"arxiv","version":2}},"canonical_sha256":"36fe2c1ad7716b32a893d2221e656b25952c3bd488b7328e3bf79b7111bda5d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36fe2c1ad7716b32a893d2221e656b25952c3bd488b7328e3bf79b7111bda5d8","first_computed_at":"2026-05-18T00:07:17.755070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.755070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RsUueBSsayIt/0DaS93zpuEKN/8j/6PTw0Q64+0LjpduMWLq1lQiqkhJZwkazRCY/6UkJYTj+Wa8svrUVZaPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.755600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06735","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2caeab956d63af2bc9c9dee4bede8b91792cc4ba81850c8d002a6b0502fcedbe","sha256:9b976dc9141608a26fcd7d86529b4ec6d3590cd450989057dd0f24775eb89cf9"],"state_sha256":"9fe256e593ad53b5c05fbe86484bc7e8d9a358b71a29778a69df24f10769b08c"}