{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4TX3RYHV63YKN7HVIWOASFSRUT","short_pith_number":"pith:4TX3RYHV","canonical_record":{"source":{"id":"1606.07702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-24T14:32:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b6161883ecc4fb41c6ec7e70230a6a9ca0f5d4e06381b64a61c4be3c357d82ce","abstract_canon_sha256":"13f4a0403038e83875129d78720696c39b44cade0047d5571bdc882c22ea3e85"},"schema_version":"1.0"},"canonical_sha256":"e4efb8e0f5f6f0a6fcf5459c091651a4d14c22c150ea62dee5c0f6531b95612a","source":{"kind":"arxiv","id":"1606.07702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07702","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07702v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07702","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"4TX3RYHV63YK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TX3RYHV63YKN7HV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TX3RYHV","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4TX3RYHV63YKN7HVIWOASFSRUT","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-24T14:32:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b6161883ecc4fb41c6ec7e70230a6a9ca0f5d4e06381b64a61c4be3c357d82ce","abstract_canon_sha256":"13f4a0403038e83875129d78720696c39b44cade0047d5571bdc882c22ea3e85"},"schema_version":"1.0"},"canonical_sha256":"e4efb8e0f5f6f0a6fcf5459c091651a4d14c22c150ea62dee5c0f6531b95612a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:59.116395Z","signature_b64":"jmfPsBxKY+DQoNO8HPvsuPGTko6mZ7STLVIro1OFoxE15RShZEP7lxM2+ooJCYf+qq9NwYkxTDwFZbJb5kD4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4efb8e0f5f6f0a6fcf5459c091651a4d14c22c150ea62dee5c0f6531b95612a","last_reissued_at":"2026-05-18T00:31:59.116008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:59.116008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07702","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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p83okcTLLozXDLvQd9WDFsTUobNhHscFm8+2ghPH786NIcLb3xWXq8eoyDRElo2TWiSUFQDHJzLQIbG806rNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T03:04:25.593365Z"},"content_sha256":"a49f19901de7297f29a60bd52c2c7e87eed77f46937b88f98f62f51baa6ffd3c","schema_version":"1.0","event_id":"sha256:a49f19901de7297f29a60bd52c2c7e87eed77f46937b88f98f62f51baa6ffd3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4TX3RYHV63YKN7HVIWOASFSRUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal adaptation for early stopping in statistical inverse problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Gilles Blanchard, Marc Hoffmann, Markus Rei{\\ss}","submitted_at":"2016-06-24T14:32:32Z","abstract_excerpt":"For linear inverse problems $Y=\\mathsf{A}\\mu+\\xi$, it is classical to recover the unknown signal $\\mu$ by iterative regularisation methods $(\\widehat \\mu^{(m)}, m=0,1,\\ldots)$ and halt at a data-dependent iteration $\\tau$ using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error $\\|\\mathsf{A}(\\widehat \\mu^{(\\tau)}-\\mu)\\|^2$ is controlled. In the context of statistical estimation with stochastic noise $\\xi$, we study oracle adaptation (that is, compared to the best possible stopping iteration) in strong squared-error $E[\\|\\hat \\mu^{(\\ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07702","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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btnJjSvHligA4dFcq4qi5KH9Zues7TzkSOUheLgmxHbNtEEN4Rbiz/SvfV9vaP5WFQxqVBwa3prAx2xS60VjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T03:04:25.593724Z"},"content_sha256":"355526dc71936b61773f92c3014026ef2c56cf98f3166e3ab3952f461b156dc6","schema_version":"1.0","event_id":"sha256:355526dc71936b61773f92c3014026ef2c56cf98f3166e3ab3952f461b156dc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TX3RYHV63YKN7HVIWOASFSRUT/bundle.json","state_url":"https://pith.science/pith/4TX3RYHV63YKN7HVIWOASFSRUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TX3RYHV63YKN7HVIWOASFSRUT/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":"2026-06-07T03:04:25Z","links":{"resolver":"https://pith.science/pith/4TX3RYHV63YKN7HVIWOASFSRUT","bundle":"https://pith.science/pith/4TX3RYHV63YKN7HVIWOASFSRUT/bundle.json","state":"https://pith.science/pith/4TX3RYHV63YKN7HVIWOASFSRUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TX3RYHV63YKN7HVIWOASFSRUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4TX3RYHV63YKN7HVIWOASFSRUT","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":"13f4a0403038e83875129d78720696c39b44cade0047d5571bdc882c22ea3e85","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-24T14:32:32Z","title_canon_sha256":"b6161883ecc4fb41c6ec7e70230a6a9ca0f5d4e06381b64a61c4be3c357d82ce"},"schema_version":"1.0","source":{"id":"1606.07702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07702","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07702v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07702","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"4TX3RYHV63YK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TX3RYHV63YKN7HV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TX3RYHV","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:355526dc71936b61773f92c3014026ef2c56cf98f3166e3ab3952f461b156dc6","target":"graph","created_at":"2026-05-18T00:31:59Z","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":"For linear inverse problems $Y=\\mathsf{A}\\mu+\\xi$, it is classical to recover the unknown signal $\\mu$ by iterative regularisation methods $(\\widehat \\mu^{(m)}, m=0,1,\\ldots)$ and halt at a data-dependent iteration $\\tau$ using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error $\\|\\mathsf{A}(\\widehat \\mu^{(\\tau)}-\\mu)\\|^2$ is controlled. In the context of statistical estimation with stochastic noise $\\xi$, we study oracle adaptation (that is, compared to the best possible stopping iteration) in strong squared-error $E[\\|\\hat \\mu^{(\\ta","authors_text":"Gilles Blanchard, Marc Hoffmann, Markus Rei{\\ss}","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-24T14:32:32Z","title":"Optimal adaptation for early stopping in statistical inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07702","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:a49f19901de7297f29a60bd52c2c7e87eed77f46937b88f98f62f51baa6ffd3c","target":"record","created_at":"2026-05-18T00:31:59Z","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":"13f4a0403038e83875129d78720696c39b44cade0047d5571bdc882c22ea3e85","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-24T14:32:32Z","title_canon_sha256":"b6161883ecc4fb41c6ec7e70230a6a9ca0f5d4e06381b64a61c4be3c357d82ce"},"schema_version":"1.0","source":{"id":"1606.07702","kind":"arxiv","version":2}},"canonical_sha256":"e4efb8e0f5f6f0a6fcf5459c091651a4d14c22c150ea62dee5c0f6531b95612a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4efb8e0f5f6f0a6fcf5459c091651a4d14c22c150ea62dee5c0f6531b95612a","first_computed_at":"2026-05-18T00:31:59.116008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:59.116008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jmfPsBxKY+DQoNO8HPvsuPGTko6mZ7STLVIro1OFoxE15RShZEP7lxM2+ooJCYf+qq9NwYkxTDwFZbJb5kD4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:59.116395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49f19901de7297f29a60bd52c2c7e87eed77f46937b88f98f62f51baa6ffd3c","sha256:355526dc71936b61773f92c3014026ef2c56cf98f3166e3ab3952f461b156dc6"],"state_sha256":"170fad810033dba49fcdef7f09fb17ec3680432a5d29f2cb773b2450f3393ef1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JE6zH+YJtmGzWwx86M4nAHEUmWhBDcsNrlecovM8Z0VOXj4lC6c/ymfvDw8/wVvFdML1c1MDiRzEI/jCSLF4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T03:04:25.595769Z","bundle_sha256":"690b97b56c29627aa7535e7418dedd9c1755950a6cd243407d4195af0df57bc3"}}