{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q32HUEVM5BHAI6G4L7FSWBXBRN","short_pith_number":"pith:Q32HUEVM","canonical_record":{"source":{"id":"1209.3628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-17T11:27:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2f432fa4e833a2e55449d71866f0a14f54664144c75f7e8da7c8a7d45a2d113b","abstract_canon_sha256":"64cc85f53a0c05281dede0be7a9dd94524f268b0560e9a2a61adcf5707686594"},"schema_version":"1.0"},"canonical_sha256":"86f47a12ace84e0478dc5fcb2b06e18b64beb14cd2f0257afd35794cce4a898d","source":{"kind":"arxiv","id":"1209.3628","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3628","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3628v2","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3628","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"Q32HUEVM5BHA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q32HUEVM5BHAI6G4","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q32HUEVM","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q32HUEVM5BHAI6G4L7FSWBXBRN","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-17T11:27:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2f432fa4e833a2e55449d71866f0a14f54664144c75f7e8da7c8a7d45a2d113b","abstract_canon_sha256":"64cc85f53a0c05281dede0be7a9dd94524f268b0560e9a2a61adcf5707686594"},"schema_version":"1.0"},"canonical_sha256":"86f47a12ace84e0478dc5fcb2b06e18b64beb14cd2f0257afd35794cce4a898d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:18.810327Z","signature_b64":"0Xg7Y9PidYOsJGOcorP+FpZJABqibyZCG8/zMJ2BiL+594R0toHmEH55i8Up1GckRzBXnLA/yT5n61zdq6FyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f47a12ace84e0478dc5fcb2b06e18b64beb14cd2f0257afd35794cce4a898d","last_reissued_at":"2026-05-18T03:22:18.809562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:18.809562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3628","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f1nY9DfFg0iSPgS8d9leJcOVstlDM5OZzHaZp513gXPVUhGNLNlt1jLODYa3V0mfah9IrjUoWlgY6g2nJgXyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:48:21.030513Z"},"content_sha256":"aa5ce6710da4b1b3805fae61cb032c0ba49143a1ededc0cff22a3a69ac841181","schema_version":"1.0","event_id":"sha256:aa5ce6710da4b1b3805fae61cb032c0ba49143a1ededc0cff22a3a69ac841181"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q32HUEVM5BHAI6G4L7FSWBXBRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayes procedures for adaptive inference in inverse problems for the white noise model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"A. W. van der Vaart, B. T. Knapik, B. T. Szab\\'o, J. H. van Zanten","submitted_at":"2012-09-17T11:27:45Z","abstract_excerpt":"We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic \"smoothness\", without using knowledge about this regularity. Both methods are illustrated by simulation examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3628","kind":"arxiv","version":2},"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":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXEDZiWcuS4HoatNXLAKhf6RF6JNrDtQNNMg2DxmrDNKuM8jieGUnLr+hgtgSUXvFrnaHcfoGdl498r0yxIMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:48:21.031071Z"},"content_sha256":"b2d8ea739d5858e82db6db1f47add9f633a84e9ddff9395de196af17e2e89fba","schema_version":"1.0","event_id":"sha256:b2d8ea739d5858e82db6db1f47add9f633a84e9ddff9395de196af17e2e89fba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/bundle.json","state_url":"https://pith.science/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/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":"2026-05-30T17:48:21Z","links":{"resolver":"https://pith.science/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN","bundle":"https://pith.science/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/bundle.json","state":"https://pith.science/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q32HUEVM5BHAI6G4L7FSWBXBRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q32HUEVM5BHAI6G4L7FSWBXBRN","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":"64cc85f53a0c05281dede0be7a9dd94524f268b0560e9a2a61adcf5707686594","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-17T11:27:45Z","title_canon_sha256":"2f432fa4e833a2e55449d71866f0a14f54664144c75f7e8da7c8a7d45a2d113b"},"schema_version":"1.0","source":{"id":"1209.3628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3628","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3628v2","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3628","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"Q32HUEVM5BHA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q32HUEVM5BHAI6G4","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q32HUEVM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:b2d8ea739d5858e82db6db1f47add9f633a84e9ddff9395de196af17e2e89fba","target":"graph","created_at":"2026-05-18T03:22:18Z","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 empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic \"smoothness\", without using knowledge about this regularity. Both methods are illustrated by simulation examples.","authors_text":"A. W. van der Vaart, B. T. Knapik, B. T. Szab\\'o, J. H. van Zanten","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-17T11:27:45Z","title":"Bayes procedures for adaptive inference in inverse problems for the white noise model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3628","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:aa5ce6710da4b1b3805fae61cb032c0ba49143a1ededc0cff22a3a69ac841181","target":"record","created_at":"2026-05-18T03:22:18Z","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":"64cc85f53a0c05281dede0be7a9dd94524f268b0560e9a2a61adcf5707686594","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-17T11:27:45Z","title_canon_sha256":"2f432fa4e833a2e55449d71866f0a14f54664144c75f7e8da7c8a7d45a2d113b"},"schema_version":"1.0","source":{"id":"1209.3628","kind":"arxiv","version":2}},"canonical_sha256":"86f47a12ace84e0478dc5fcb2b06e18b64beb14cd2f0257afd35794cce4a898d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86f47a12ace84e0478dc5fcb2b06e18b64beb14cd2f0257afd35794cce4a898d","first_computed_at":"2026-05-18T03:22:18.809562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:18.809562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Xg7Y9PidYOsJGOcorP+FpZJABqibyZCG8/zMJ2BiL+594R0toHmEH55i8Up1GckRzBXnLA/yT5n61zdq6FyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:18.810327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa5ce6710da4b1b3805fae61cb032c0ba49143a1ededc0cff22a3a69ac841181","sha256:b2d8ea739d5858e82db6db1f47add9f633a84e9ddff9395de196af17e2e89fba"],"state_sha256":"4cbc0be150a8150c81970bcce85b489271de512c51594b740ee6fe341a8a8e8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yC6d9+/MjCY0jfjqDdKu2h0LX/ow40sW4OsfIhZwOs8I/SsoWjEdBB9iYRt/DIFquxweQ1MTHaw7Jcz0Nl+zAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:48:21.034068Z","bundle_sha256":"4372826cd5417bb3a8f0164c981c91e9faf4a9ac21c029a5a3f6137ea4c5b208"}}