{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6ZTTN5YNB3QOYAZNJVYPOD2MSI","short_pith_number":"pith:6ZTTN5YN","canonical_record":{"source":{"id":"1607.04879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-17T15:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"102daa1cd52d1eb3f04c3fe59ab1df83a0b80fe5e65e558bee79fd374a02dc7d","abstract_canon_sha256":"bc588b704a52db419d933970aece4e2f679af932312e3ce49dd31cff2d29baf7"},"schema_version":"1.0"},"canonical_sha256":"f66736f70d0ee0ec032d4d70f70f4c923940a1cc3b6ed971e87e3c82fa59edec","source":{"kind":"arxiv","id":"1607.04879","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04879","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04879v1","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04879","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"6ZTTN5YNB3QO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6ZTTN5YNB3QOYAZN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6ZTTN5YN","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6ZTTN5YNB3QOYAZNJVYPOD2MSI","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-17T15:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"102daa1cd52d1eb3f04c3fe59ab1df83a0b80fe5e65e558bee79fd374a02dc7d","abstract_canon_sha256":"bc588b704a52db419d933970aece4e2f679af932312e3ce49dd31cff2d29baf7"},"schema_version":"1.0"},"canonical_sha256":"f66736f70d0ee0ec032d4d70f70f4c923940a1cc3b6ed971e87e3c82fa59edec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:56.459746Z","signature_b64":"GNluzt3w/vE2VBa8vV8jukvV6KZUzx+8k1KAgmQoT9TLeCteStNrtfbVP4UyqC/5rM0uuPgSGQL5Xu2M71jAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f66736f70d0ee0ec032d4d70f70f4c923940a1cc3b6ed971e87e3c82fa59edec","last_reissued_at":"2026-05-18T01:10:56.455429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:56.455429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04879","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":"2026-05-18T01:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2mN7nMYaB+sapZp5J3AfvaKrK7IU1Rh0HHToLbsh0Gher1Nt79mC5yFDNVa2pn9TbxrwsDho/Tld4Azl73KBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:18:38.829355Z"},"content_sha256":"2ba27a37103d61807b18b89bd6980c079d48ce8130094019018524a877763f44","schema_version":"1.0","event_id":"sha256:2ba27a37103d61807b18b89bd6980c079d48ce8130094019018524a877763f44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6ZTTN5YNB3QOYAZNJVYPOD2MSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Robert Plato","submitted_at":"2016-07-17T15:28:14Z","abstract_excerpt":"This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturation results which are an important part in regularization theory. As a byproduct we obtain a new result on the quasi-optimality of a posteriori parameter choices. Results in this paper are formulated in Banach spaces whenever possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04879","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":"2026-05-18T01:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BvnijV5nGqhjN4vBbOWqZw4efp8fy8HfbWuzsmDJc4b8tUzTn2M6k77v/2bXC0oSjihKI21DcCphiftwb9r4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:18:38.829692Z"},"content_sha256":"f96963db686edd764e3871524ecf50899c956c1964b972177bb22ebfaa2ae999","schema_version":"1.0","event_id":"sha256:f96963db686edd764e3871524ecf50899c956c1964b972177bb22ebfaa2ae999"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/bundle.json","state_url":"https://pith.science/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/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":"2026-06-20T08:18:38Z","links":{"resolver":"https://pith.science/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI","bundle":"https://pith.science/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/bundle.json","state":"https://pith.science/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZTTN5YNB3QOYAZNJVYPOD2MSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6ZTTN5YNB3QOYAZNJVYPOD2MSI","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":"bc588b704a52db419d933970aece4e2f679af932312e3ce49dd31cff2d29baf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-17T15:28:14Z","title_canon_sha256":"102daa1cd52d1eb3f04c3fe59ab1df83a0b80fe5e65e558bee79fd374a02dc7d"},"schema_version":"1.0","source":{"id":"1607.04879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04879","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04879v1","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04879","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"6ZTTN5YNB3QO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6ZTTN5YNB3QOYAZN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6ZTTN5YN","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:f96963db686edd764e3871524ecf50899c956c1964b972177bb22ebfaa2ae999","target":"graph","created_at":"2026-05-18T01:10:56Z","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":"This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturation results which are an important part in regularization theory. As a byproduct we obtain a new result on the quasi-optimality of a posteriori parameter choices. Results in this paper are formulated in Banach spaces whenever possible.","authors_text":"Robert Plato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-17T15:28:14Z","title":"Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04879","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":"sha256:2ba27a37103d61807b18b89bd6980c079d48ce8130094019018524a877763f44","target":"record","created_at":"2026-05-18T01:10:56Z","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":"bc588b704a52db419d933970aece4e2f679af932312e3ce49dd31cff2d29baf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-17T15:28:14Z","title_canon_sha256":"102daa1cd52d1eb3f04c3fe59ab1df83a0b80fe5e65e558bee79fd374a02dc7d"},"schema_version":"1.0","source":{"id":"1607.04879","kind":"arxiv","version":1}},"canonical_sha256":"f66736f70d0ee0ec032d4d70f70f4c923940a1cc3b6ed971e87e3c82fa59edec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f66736f70d0ee0ec032d4d70f70f4c923940a1cc3b6ed971e87e3c82fa59edec","first_computed_at":"2026-05-18T01:10:56.455429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:56.455429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GNluzt3w/vE2VBa8vV8jukvV6KZUzx+8k1KAgmQoT9TLeCteStNrtfbVP4UyqC/5rM0uuPgSGQL5Xu2M71jAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:56.459746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba27a37103d61807b18b89bd6980c079d48ce8130094019018524a877763f44","sha256:f96963db686edd764e3871524ecf50899c956c1964b972177bb22ebfaa2ae999"],"state_sha256":"b3104b94f62b0ff85860282dff6fc1b381b26ddcfcbf9f8a34d861b348c3155c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHL+/9VWtI4FiHptkNxsSQXWmE2p4ZHM9R/mi3OnryDyTZ+5FjeymDe7uSRrMNl/4WgtiEsLWeS3+L3XfFhjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:18:38.831634Z","bundle_sha256":"78fc8b8f13e679a5216dec2a5c8aa7e3187963543f5ef37a4fac5ed107da510f"}}