{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SU3LWMKSCIQL6ZKJV77LBGUDD7","short_pith_number":"pith:SU3LWMKS","canonical_record":{"source":{"id":"1601.05766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-01-21T20:17:23Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e3d5283b2f27faa5dbaf2b9969360fab579a6b43bba25de80d0310e747f67c79","abstract_canon_sha256":"8f699686fed22eae7683dfe8915fe6d5a8b673c5734e55c53bd0ed903f6992bd"},"schema_version":"1.0"},"canonical_sha256":"9536bb31521220bf6549affeb09a831ff8bf34c2506047c50248fa3118b7fc6a","source":{"kind":"arxiv","id":"1601.05766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05766","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05766v2","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05766","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"SU3LWMKSCIQL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SU3LWMKSCIQL6ZKJ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SU3LWMKS","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SU3LWMKSCIQL6ZKJV77LBGUDD7","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-01-21T20:17:23Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e3d5283b2f27faa5dbaf2b9969360fab579a6b43bba25de80d0310e747f67c79","abstract_canon_sha256":"8f699686fed22eae7683dfe8915fe6d5a8b673c5734e55c53bd0ed903f6992bd"},"schema_version":"1.0"},"canonical_sha256":"9536bb31521220bf6549affeb09a831ff8bf34c2506047c50248fa3118b7fc6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:06.572696Z","signature_b64":"v3lPo5cuIOR44voc8/p8bdIUvH4UP32kn0B7mjiEov70re44+fBybXQgHGquj92HrBof4DgzwagJWSV5HrWfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9536bb31521220bf6549affeb09a831ff8bf34c2506047c50248fa3118b7fc6a","last_reissued_at":"2026-05-17T23:49:06.572045Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:06.572045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05766","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":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aBac7qpL++ceTF2zXdHqsPZPM5C71vIx6LuO+tE0WVV32XpGQk/iJnSQyE2Opq7IEPNfAKP5TpMA+iaicbVrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:44:10.992086Z"},"content_sha256":"564bff84a2351200b4c10237083c90779aa25c1f0bd9ebce47ba06e42fed8b64","schema_version":"1.0","event_id":"sha256:564bff84a2351200b4c10237083c90779aa25c1f0bd9ebce47ba06e42fed8b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SU3LWMKSCIQL6ZKJV77LBGUDD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive confidence sets in shape restricted regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Pierre C. Bellec","submitted_at":"2016-01-21T20:17:23Z","abstract_excerpt":"A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the proposed confidence set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, the diameter of the proposed confidence set automatically adapts to the unknown number of pieces of the true parameter, in the sense that the diameter is bounded from above by the minimax risk over the class of $k$-piecewise constant functions. The diameter of the confidence set is a simple increasing function of the number of jumps of the isoto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05766","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":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eGZG8+P+LSxxbue+elNAZdMmvWmsF20ZJJAgrE3Bv+dr3FlZ5KaOsHfhPCm3JMHnubvRHVRddyQfyRDymiaADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:44:10.992439Z"},"content_sha256":"5db4f395b6e99177c095544796ce475056b933f97adfa26491ceae38ad08ba7d","schema_version":"1.0","event_id":"sha256:5db4f395b6e99177c095544796ce475056b933f97adfa26491ceae38ad08ba7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/bundle.json","state_url":"https://pith.science/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/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":"2026-06-12T10:44:10Z","links":{"resolver":"https://pith.science/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7","bundle":"https://pith.science/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/bundle.json","state":"https://pith.science/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SU3LWMKSCIQL6ZKJV77LBGUDD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SU3LWMKSCIQL6ZKJV77LBGUDD7","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":"8f699686fed22eae7683dfe8915fe6d5a8b673c5734e55c53bd0ed903f6992bd","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-01-21T20:17:23Z","title_canon_sha256":"e3d5283b2f27faa5dbaf2b9969360fab579a6b43bba25de80d0310e747f67c79"},"schema_version":"1.0","source":{"id":"1601.05766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05766","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05766v2","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05766","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"SU3LWMKSCIQL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SU3LWMKSCIQL6ZKJ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SU3LWMKS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:5db4f395b6e99177c095544796ce475056b933f97adfa26491ceae38ad08ba7d","target":"graph","created_at":"2026-05-17T23:49:06Z","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":"A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the proposed confidence set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, the diameter of the proposed confidence set automatically adapts to the unknown number of pieces of the true parameter, in the sense that the diameter is bounded from above by the minimax risk over the class of $k$-piecewise constant functions. The diameter of the confidence set is a simple increasing function of the number of jumps of the isoto","authors_text":"Pierre C. Bellec","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-01-21T20:17:23Z","title":"Adaptive confidence sets in shape restricted regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05766","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":"sha256:564bff84a2351200b4c10237083c90779aa25c1f0bd9ebce47ba06e42fed8b64","target":"record","created_at":"2026-05-17T23:49:06Z","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":"8f699686fed22eae7683dfe8915fe6d5a8b673c5734e55c53bd0ed903f6992bd","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-01-21T20:17:23Z","title_canon_sha256":"e3d5283b2f27faa5dbaf2b9969360fab579a6b43bba25de80d0310e747f67c79"},"schema_version":"1.0","source":{"id":"1601.05766","kind":"arxiv","version":2}},"canonical_sha256":"9536bb31521220bf6549affeb09a831ff8bf34c2506047c50248fa3118b7fc6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9536bb31521220bf6549affeb09a831ff8bf34c2506047c50248fa3118b7fc6a","first_computed_at":"2026-05-17T23:49:06.572045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.572045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v3lPo5cuIOR44voc8/p8bdIUvH4UP32kn0B7mjiEov70re44+fBybXQgHGquj92HrBof4DgzwagJWSV5HrWfBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.572696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:564bff84a2351200b4c10237083c90779aa25c1f0bd9ebce47ba06e42fed8b64","sha256:5db4f395b6e99177c095544796ce475056b933f97adfa26491ceae38ad08ba7d"],"state_sha256":"2bf56f6bea6267c2d79b7e80947cd7e62b159166ac3f0b9431317d05f3bc2f5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzlvJ2ccKXdJ6d9OGaSRK321A/8LEmro1088u8r2ZPOmOiuhoIkLNzAERnv07jwTs9fBlCkbhtZb6DvEA04RCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:44:10.994608Z","bundle_sha256":"7a749e1dde18a7cb223c6b1145923e6c11dca2f49ab30e47645c010640e9a55b"}}