{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:O6QXN3PFKCBVRJLUSG4IFUQ2LQ","short_pith_number":"pith:O6QXN3PF","canonical_record":{"source":{"id":"1111.5568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-23T17:43:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6f828748d087e47f1b92a708767c731be4c49a21eb9f9e05bc0f0a4ed5f6b699","abstract_canon_sha256":"e4ff8746546ea0efe867113ad0fa4cda215d247342053dc081510678dce60632"},"schema_version":"1.0"},"canonical_sha256":"77a176ede5508358a57491b882d21a5c070b7c6d0e11f5591fec8ddb90aa5fb1","source":{"kind":"arxiv","id":"1111.5568","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5568","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5568v3","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5568","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"O6QXN3PFKCBV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O6QXN3PFKCBVRJLU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O6QXN3PF","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:O6QXN3PFKCBVRJLUSG4IFUQ2LQ","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-23T17:43:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6f828748d087e47f1b92a708767c731be4c49a21eb9f9e05bc0f0a4ed5f6b699","abstract_canon_sha256":"e4ff8746546ea0efe867113ad0fa4cda215d247342053dc081510678dce60632"},"schema_version":"1.0"},"canonical_sha256":"77a176ede5508358a57491b882d21a5c070b7c6d0e11f5591fec8ddb90aa5fb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:14.089975Z","signature_b64":"K74oIu3BoSvjH5awv1y6i1xDEjyMjJ6iLeRTYvWXGR8mXhQ2dw+IQ7uSNtij62llWh/9/EJMsV/IB2dakJmEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77a176ede5508358a57491b882d21a5c070b7c6d0e11f5591fec8ddb90aa5fb1","last_reissued_at":"2026-05-18T03:04:14.089535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:14.089535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5568","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xf03ozM1qWWELbJpVpICcxWawcl3ReOKmNrUfC3p2jF8d8T78fTw0wU/73oHruoNN7Q+bBYy2LzpdVilUAMmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:33:52.993640Z"},"content_sha256":"12ba7e3f4e329b359b9a34fdb6569479eb85b1fd9486bc6da3a09741a967f2ec","schema_version":"1.0","event_id":"sha256:12ba7e3f4e329b359b9a34fdb6569479eb85b1fd9486bc6da3a09741a967f2ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:O6QXN3PFKCBVRJLUSG4IFUQ2LQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive confidence sets in L^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Adam D. Bull, Richard Nickl","submitted_at":"2011-11-23T17:43:03Z","abstract_excerpt":"The problem of constructing confidence sets that are adaptive in L^2-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev ball and its smoothness degree, and over maximal parameter spaces for which adaptation is possible. Two key regimes of parameter constellations are identified: one where full adaptation is possible, and one where adaptation requires critical regions be removed. Techniques used to derive these results include a general nonparametric minimax test for infinite-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5568","kind":"arxiv","version":3},"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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZ8zeZ7CjZxiCsHau6mfBgCtYP43WemMGOa5FDsu3cTWb18+BdEzZzJ2WWgispeulTPnnm6vb39X3wkm4vkrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:33:52.994306Z"},"content_sha256":"8c1e250679ece1bc7f89f075088ccd7f04c630cf83ab0baef95bc7e21d287da3","schema_version":"1.0","event_id":"sha256:8c1e250679ece1bc7f89f075088ccd7f04c630cf83ab0baef95bc7e21d287da3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/bundle.json","state_url":"https://pith.science/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/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":"2026-05-31T14:33:52Z","links":{"resolver":"https://pith.science/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ","bundle":"https://pith.science/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/bundle.json","state":"https://pith.science/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6QXN3PFKCBVRJLUSG4IFUQ2LQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O6QXN3PFKCBVRJLUSG4IFUQ2LQ","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":"e4ff8746546ea0efe867113ad0fa4cda215d247342053dc081510678dce60632","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-23T17:43:03Z","title_canon_sha256":"6f828748d087e47f1b92a708767c731be4c49a21eb9f9e05bc0f0a4ed5f6b699"},"schema_version":"1.0","source":{"id":"1111.5568","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5568","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5568v3","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5568","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"O6QXN3PFKCBV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O6QXN3PFKCBVRJLU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O6QXN3PF","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:8c1e250679ece1bc7f89f075088ccd7f04c630cf83ab0baef95bc7e21d287da3","target":"graph","created_at":"2026-05-18T03:04:14Z","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":"The problem of constructing confidence sets that are adaptive in L^2-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev ball and its smoothness degree, and over maximal parameter spaces for which adaptation is possible. Two key regimes of parameter constellations are identified: one where full adaptation is possible, and one where adaptation requires critical regions be removed. Techniques used to derive these results include a general nonparametric minimax test for infinite-di","authors_text":"Adam D. Bull, Richard Nickl","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-23T17:43:03Z","title":"Adaptive confidence sets in L^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5568","kind":"arxiv","version":3},"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":"sha256:12ba7e3f4e329b359b9a34fdb6569479eb85b1fd9486bc6da3a09741a967f2ec","target":"record","created_at":"2026-05-18T03:04:14Z","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":"e4ff8746546ea0efe867113ad0fa4cda215d247342053dc081510678dce60632","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-23T17:43:03Z","title_canon_sha256":"6f828748d087e47f1b92a708767c731be4c49a21eb9f9e05bc0f0a4ed5f6b699"},"schema_version":"1.0","source":{"id":"1111.5568","kind":"arxiv","version":3}},"canonical_sha256":"77a176ede5508358a57491b882d21a5c070b7c6d0e11f5591fec8ddb90aa5fb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a176ede5508358a57491b882d21a5c070b7c6d0e11f5591fec8ddb90aa5fb1","first_computed_at":"2026-05-18T03:04:14.089535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.089535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K74oIu3BoSvjH5awv1y6i1xDEjyMjJ6iLeRTYvWXGR8mXhQ2dw+IQ7uSNtij62llWh/9/EJMsV/IB2dakJmEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.089975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5568","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12ba7e3f4e329b359b9a34fdb6569479eb85b1fd9486bc6da3a09741a967f2ec","sha256:8c1e250679ece1bc7f89f075088ccd7f04c630cf83ab0baef95bc7e21d287da3"],"state_sha256":"2220b776056b3223fee27cd5ba76118df38b18f87c70f0300738af0382df3060"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DC2xy6+Md3TqS7Maxevd+m3sXU7Xe+p+NluRTvEgglQYKXdLxSBYaIfgLG4A19202odKzu8Qi3+pRf2182XrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:33:52.997926Z","bundle_sha256":"74389c711e9aebbf62271cdf4746f4298c9b62972cf3b861531348ee56b948e5"}}