{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:K5HKN5H34FD2A7TGEKHMACYEMD","short_pith_number":"pith:K5HKN5H3","canonical_record":{"source":{"id":"1104.1050","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-06T10:00:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6cded02c66583297bfdfd7d5f15d9edecac3899ea5b038e66f5a08a46cb205f7","abstract_canon_sha256":"b87d125c957e5dad68537c60d998e7070dc8f20ebf0547c842fd4cbcc3bc07be"},"schema_version":"1.0"},"canonical_sha256":"574ea6f4fbe147a07e66228ec00b0460c00674cf77219057c4933469af51a98a","source":{"kind":"arxiv","id":"1104.1050","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1050","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1050v2","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1050","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"K5HKN5H34FD2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5HKN5H34FD2A7TG","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5HKN5H3","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:K5HKN5H34FD2A7TGEKHMACYEMD","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1050","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-06T10:00:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6cded02c66583297bfdfd7d5f15d9edecac3899ea5b038e66f5a08a46cb205f7","abstract_canon_sha256":"b87d125c957e5dad68537c60d998e7070dc8f20ebf0547c842fd4cbcc3bc07be"},"schema_version":"1.0"},"canonical_sha256":"574ea6f4fbe147a07e66228ec00b0460c00674cf77219057c4933469af51a98a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:51.587500Z","signature_b64":"EzCJtWjXzZQk4nCWNLFUhnbF/ywgm1Qw3ygbgweAdJHdmyqZfLcUo1krRrZD8bQVdHtbJfTp+JbIhT0bm5H7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"574ea6f4fbe147a07e66228ec00b0460c00674cf77219057c4933469af51a98a","last_reissued_at":"2026-05-18T01:37:51.586839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:51.586839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1050","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":"2026-05-18T01:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdXzA98o2o6+5KYJ7F8toIgAEgJafvIPIh7MA12zBfnEHL2fMtWjcEKsT3gb3Gd9SiRUxNjfcIYIoFZ6lWVYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:53.927187Z"},"content_sha256":"52ed8e870921e78d1d2edb32b55f79dfd115b6792e868950e87b6a301cad5e64","schema_version":"1.0","event_id":"sha256:52ed8e870921e78d1d2edb32b55f79dfd115b6792e868950e87b6a301cad5e64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:K5HKN5H34FD2A7TGEKHMACYEMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Slope Heuristics in Heteroscedastic Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Adrien Saumard","submitted_at":"2011-04-06T10:00:37Z","abstract_excerpt":"We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is estimated by using a penalized least-squares model selection method. In this context, we show the existence of a minimal penalty, defined to be the maximum level of penalization under which the model selection procedure totally misbehaves. The optimal penalty is shown to be twice the minimal one and to satisfy a non-asymptotic pathwise oracle inequality with leadi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1050","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":"2026-05-18T01:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxcKoL1u+BupwjOu7o8f22ht/q6OsIJlP66wwKrOziuqolOTkw33G5FMm1B4a2sL491AcrUvz2s32WFR+JZqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:53.927698Z"},"content_sha256":"db934eec6be05ce9f5f1dd6062f8229898952a1ec6e82380e2493b90efdb6b50","schema_version":"1.0","event_id":"sha256:db934eec6be05ce9f5f1dd6062f8229898952a1ec6e82380e2493b90efdb6b50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5HKN5H34FD2A7TGEKHMACYEMD/bundle.json","state_url":"https://pith.science/pith/K5HKN5H34FD2A7TGEKHMACYEMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5HKN5H34FD2A7TGEKHMACYEMD/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":"2026-05-27T15:52:53Z","links":{"resolver":"https://pith.science/pith/K5HKN5H34FD2A7TGEKHMACYEMD","bundle":"https://pith.science/pith/K5HKN5H34FD2A7TGEKHMACYEMD/bundle.json","state":"https://pith.science/pith/K5HKN5H34FD2A7TGEKHMACYEMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5HKN5H34FD2A7TGEKHMACYEMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5HKN5H34FD2A7TGEKHMACYEMD","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":"b87d125c957e5dad68537c60d998e7070dc8f20ebf0547c842fd4cbcc3bc07be","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-06T10:00:37Z","title_canon_sha256":"6cded02c66583297bfdfd7d5f15d9edecac3899ea5b038e66f5a08a46cb205f7"},"schema_version":"1.0","source":{"id":"1104.1050","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1050","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1050v2","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1050","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"K5HKN5H34FD2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5HKN5H34FD2A7TG","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5HKN5H3","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:db934eec6be05ce9f5f1dd6062f8229898952a1ec6e82380e2493b90efdb6b50","target":"graph","created_at":"2026-05-18T01:37:51Z","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 consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is estimated by using a penalized least-squares model selection method. In this context, we show the existence of a minimal penalty, defined to be the maximum level of penalization under which the model selection procedure totally misbehaves. The optimal penalty is shown to be twice the minimal one and to satisfy a non-asymptotic pathwise oracle inequality with leadi","authors_text":"Adrien Saumard","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-06T10:00:37Z","title":"The Slope Heuristics in Heteroscedastic Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1050","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":"sha256:52ed8e870921e78d1d2edb32b55f79dfd115b6792e868950e87b6a301cad5e64","target":"record","created_at":"2026-05-18T01:37:51Z","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":"b87d125c957e5dad68537c60d998e7070dc8f20ebf0547c842fd4cbcc3bc07be","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-06T10:00:37Z","title_canon_sha256":"6cded02c66583297bfdfd7d5f15d9edecac3899ea5b038e66f5a08a46cb205f7"},"schema_version":"1.0","source":{"id":"1104.1050","kind":"arxiv","version":2}},"canonical_sha256":"574ea6f4fbe147a07e66228ec00b0460c00674cf77219057c4933469af51a98a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"574ea6f4fbe147a07e66228ec00b0460c00674cf77219057c4933469af51a98a","first_computed_at":"2026-05-18T01:37:51.586839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:51.586839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EzCJtWjXzZQk4nCWNLFUhnbF/ywgm1Qw3ygbgweAdJHdmyqZfLcUo1krRrZD8bQVdHtbJfTp+JbIhT0bm5H7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:51.587500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1050","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52ed8e870921e78d1d2edb32b55f79dfd115b6792e868950e87b6a301cad5e64","sha256:db934eec6be05ce9f5f1dd6062f8229898952a1ec6e82380e2493b90efdb6b50"],"state_sha256":"47cde527dae0a21f893455c2a5c2fc13d1a4fad089c1b29d120424203ac36b9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tMF4GrhJHHlkMXShZxFfUbJzAiuS0GCobtjTvqyg5PY8E0jq19bK8dv3UkN4Wv85NVH/3nX/sAaw2G3/J01Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:52:53.930554Z","bundle_sha256":"706d770af30fee3a5bd6189968f3edab32e3371f8ed360c1e51f0e8435c420cf"}}