{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HVXVY3QDUDF3PW4Y436NETMEBC","short_pith_number":"pith:HVXVY3QD","canonical_record":{"source":{"id":"1011.3669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-16T12:19:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5bfd72285b085adc1133d0874e8520a21b30c9028ac4469d487e25e19e1dcadc","abstract_canon_sha256":"af2d5b95131b9f6cfdc0d786933a7191501cc673f86f61ade978578182ddae3b"},"schema_version":"1.0"},"canonical_sha256":"3d6f5c6e03a0cbb7db98e6fcd24d8408b66fd057517f5b7b5caf8ce38d7014ee","source":{"kind":"arxiv","id":"1011.3669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3669","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3669v1","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3669","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"HVXVY3QDUDF3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HVXVY3QDUDF3PW4Y","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HVXVY3QD","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HVXVY3QDUDF3PW4Y436NETMEBC","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-16T12:19:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5bfd72285b085adc1133d0874e8520a21b30c9028ac4469d487e25e19e1dcadc","abstract_canon_sha256":"af2d5b95131b9f6cfdc0d786933a7191501cc673f86f61ade978578182ddae3b"},"schema_version":"1.0"},"canonical_sha256":"3d6f5c6e03a0cbb7db98e6fcd24d8408b66fd057517f5b7b5caf8ce38d7014ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:45.259466Z","signature_b64":"WjQRgpgtco784LuD27ORFV0nqKJxUpyJTXkXgNU/JoNFTGE2+mlXKwoA0Vj7gX+X6q6mWgOEP3G1QUPjI6QsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d6f5c6e03a0cbb7db98e6fcd24d8408b66fd057517f5b7b5caf8ce38d7014ee","last_reissued_at":"2026-05-18T02:04:45.258606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:45.258606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3669","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":"2026-05-18T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biSz5IMJJF1MK0nJV/ahsywpvgfbWgrxCo8FvUaUORZXGpNUsArREDlTVJ3+lBDuEMq0e5GPhrNgG1bhqlVACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:46:58.957838Z"},"content_sha256":"206d599634ade23f3e0cdc696a37fe34ce719d09e6722946fc55fea798bb5450","schema_version":"1.0","event_id":"sha256:206d599634ade23f3e0cdc696a37fe34ce719d09e6722946fc55fea798bb5450"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HVXVY3QDUDF3PW4Y436NETMEBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularization of statistical inverse problems and the Bakushinskii veto","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Saskia Becker","submitted_at":"2010-11-16T12:19:13Z","abstract_excerpt":"In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3669","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":"2026-05-18T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZXJG9pHsx98PnBveR7YKzIB+NBWGFu/TmLKUeV8Rz+D+gSCeKuQ8myRIAOHHq4yz29CnZNqx4u11iNdcpQ2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:46:58.958177Z"},"content_sha256":"2d3d994962fa2158fe2f00e9813a2e82cfa23622d2a6bdb576a57f67295dd2a8","schema_version":"1.0","event_id":"sha256:2d3d994962fa2158fe2f00e9813a2e82cfa23622d2a6bdb576a57f67295dd2a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVXVY3QDUDF3PW4Y436NETMEBC/bundle.json","state_url":"https://pith.science/pith/HVXVY3QDUDF3PW4Y436NETMEBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVXVY3QDUDF3PW4Y436NETMEBC/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":"2026-06-20T18:46:58Z","links":{"resolver":"https://pith.science/pith/HVXVY3QDUDF3PW4Y436NETMEBC","bundle":"https://pith.science/pith/HVXVY3QDUDF3PW4Y436NETMEBC/bundle.json","state":"https://pith.science/pith/HVXVY3QDUDF3PW4Y436NETMEBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVXVY3QDUDF3PW4Y436NETMEBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HVXVY3QDUDF3PW4Y436NETMEBC","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":"af2d5b95131b9f6cfdc0d786933a7191501cc673f86f61ade978578182ddae3b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-16T12:19:13Z","title_canon_sha256":"5bfd72285b085adc1133d0874e8520a21b30c9028ac4469d487e25e19e1dcadc"},"schema_version":"1.0","source":{"id":"1011.3669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3669","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3669v1","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3669","created_at":"2026-05-18T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"HVXVY3QDUDF3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HVXVY3QDUDF3PW4Y","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HVXVY3QD","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2d3d994962fa2158fe2f00e9813a2e82cfa23622d2a6bdb576a57f67295dd2a8","target":"graph","created_at":"2026-05-18T02:04:45Z","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 the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical","authors_text":"Saskia Becker","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-16T12:19:13Z","title":"Regularization of statistical inverse problems and the Bakushinskii veto"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3669","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":"sha256:206d599634ade23f3e0cdc696a37fe34ce719d09e6722946fc55fea798bb5450","target":"record","created_at":"2026-05-18T02:04:45Z","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":"af2d5b95131b9f6cfdc0d786933a7191501cc673f86f61ade978578182ddae3b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-16T12:19:13Z","title_canon_sha256":"5bfd72285b085adc1133d0874e8520a21b30c9028ac4469d487e25e19e1dcadc"},"schema_version":"1.0","source":{"id":"1011.3669","kind":"arxiv","version":1}},"canonical_sha256":"3d6f5c6e03a0cbb7db98e6fcd24d8408b66fd057517f5b7b5caf8ce38d7014ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d6f5c6e03a0cbb7db98e6fcd24d8408b66fd057517f5b7b5caf8ce38d7014ee","first_computed_at":"2026-05-18T02:04:45.258606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:45.258606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WjQRgpgtco784LuD27ORFV0nqKJxUpyJTXkXgNU/JoNFTGE2+mlXKwoA0Vj7gX+X6q6mWgOEP3G1QUPjI6QsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:45.259466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:206d599634ade23f3e0cdc696a37fe34ce719d09e6722946fc55fea798bb5450","sha256:2d3d994962fa2158fe2f00e9813a2e82cfa23622d2a6bdb576a57f67295dd2a8"],"state_sha256":"0c807e90a22daf5217587491fd0f0cb21b8df80083381e2b6803b03d80c3d02f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1SmCqT45ndIgGi/cajGGGcqambEvzAiZx164k7udeKeroKtL8to8NPI8OKekbrFts3f5iVwI/2Bjrq6apzP7Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:46:58.960166Z","bundle_sha256":"bf631c75150432ff6e44ec017ec0bc441277c6412ae586dc7f8f8963c2c335bb"}}