{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QNN7H37ZYRU5EHOINKLNJUPUCH","short_pith_number":"pith:QNN7H37Z","canonical_record":{"source":{"id":"1205.0023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-30T20:09:11Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e3408e2ab23813d699d5f364c70f343790c7134c846eaec1d0f1b025beb654ef","abstract_canon_sha256":"af112abe1a3622cd102b0d2938a4cc48bd120c2080ff9ab1daced59f23296469"},"schema_version":"1.0"},"canonical_sha256":"835bf3eff9c469d21dc86a96d4d1f411f3cef130d97a3532386788e4b667054a","source":{"kind":"arxiv","id":"1205.0023","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0023","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0023v1","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0023","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"QNN7H37ZYRU5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QNN7H37ZYRU5EHOI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QNN7H37Z","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QNN7H37ZYRU5EHOINKLNJUPUCH","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-30T20:09:11Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e3408e2ab23813d699d5f364c70f343790c7134c846eaec1d0f1b025beb654ef","abstract_canon_sha256":"af112abe1a3622cd102b0d2938a4cc48bd120c2080ff9ab1daced59f23296469"},"schema_version":"1.0"},"canonical_sha256":"835bf3eff9c469d21dc86a96d4d1f411f3cef130d97a3532386788e4b667054a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:36.002695Z","signature_b64":"MrF4D3k+/ctGBTtHhClv7gRbmNkzO3UHSHBNzMHbS/GGnSrKHl1MW3OipyHgZrss3V/U6q15CaQpASaGrPZRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"835bf3eff9c469d21dc86a96d4d1f411f3cef130d97a3532386788e4b667054a","last_reissued_at":"2026-05-18T03:56:36.002011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:36.002011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0023","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7C4D+0CgJKFGS9yrdxqwmao7ty8lF4ySPvDHUSvwz5wfQm6kppcXvc0VR+djlRJKi2kuTk4AGeaIk3fbaVfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:46.167722Z"},"content_sha256":"b5dc072d0baf90aa92fcfc569b6454c3433383d0bb3cc7f7e6e8348bf9778fe3","schema_version":"1.0","event_id":"sha256:b5dc072d0baf90aa92fcfc569b6454c3433383d0bb3cc7f7e6e8348bf9778fe3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QNN7H37ZYRU5EHOINKLNJUPUCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform Convergence and Rate Adaptive Estimation of a Convex Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jinglai Shen, Xiao Wang","submitted_at":"2012-04-30T20:09:11Z","abstract_excerpt":"This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the $\\ell_\\infty$-norm by exploiting piecewise linear and polyhedral theory. Based upon this property, it is shown that this estimator attains optimal rates of convergence on the entire interval of interest over the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0023","kind":"arxiv","version":1},"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":"2026-05-18T03:56:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOYfPTGbESgIRzMBXgBT5UnhVSF+mx+hBzPOexa4thqiWAjoPBfaw29+RlBvPp9iNYuKYsoBK9lEtyPdBO6CBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:46.168675Z"},"content_sha256":"a96e8e3d1b7be3013470daee4eb09ec76d61ada66800de5bad486120f0959e38","schema_version":"1.0","event_id":"sha256:a96e8e3d1b7be3013470daee4eb09ec76d61ada66800de5bad486120f0959e38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/bundle.json","state_url":"https://pith.science/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/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":"2026-06-11T08:48:46Z","links":{"resolver":"https://pith.science/pith/QNN7H37ZYRU5EHOINKLNJUPUCH","bundle":"https://pith.science/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/bundle.json","state":"https://pith.science/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNN7H37ZYRU5EHOINKLNJUPUCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QNN7H37ZYRU5EHOINKLNJUPUCH","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":"af112abe1a3622cd102b0d2938a4cc48bd120c2080ff9ab1daced59f23296469","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-30T20:09:11Z","title_canon_sha256":"e3408e2ab23813d699d5f364c70f343790c7134c846eaec1d0f1b025beb654ef"},"schema_version":"1.0","source":{"id":"1205.0023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0023","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0023v1","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0023","created_at":"2026-05-18T03:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"QNN7H37ZYRU5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QNN7H37ZYRU5EHOI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QNN7H37Z","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:a96e8e3d1b7be3013470daee4eb09ec76d61ada66800de5bad486120f0959e38","target":"graph","created_at":"2026-05-18T03:56:36Z","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":"This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the $\\ell_\\infty$-norm by exploiting piecewise linear and polyhedral theory. Based upon this property, it is shown that this estimator attains optimal rates of convergence on the entire interval of interest over the ","authors_text":"Jinglai Shen, Xiao Wang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-30T20:09:11Z","title":"Uniform Convergence and Rate Adaptive Estimation of a Convex Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0023","kind":"arxiv","version":1},"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:b5dc072d0baf90aa92fcfc569b6454c3433383d0bb3cc7f7e6e8348bf9778fe3","target":"record","created_at":"2026-05-18T03:56:36Z","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":"af112abe1a3622cd102b0d2938a4cc48bd120c2080ff9ab1daced59f23296469","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-30T20:09:11Z","title_canon_sha256":"e3408e2ab23813d699d5f364c70f343790c7134c846eaec1d0f1b025beb654ef"},"schema_version":"1.0","source":{"id":"1205.0023","kind":"arxiv","version":1}},"canonical_sha256":"835bf3eff9c469d21dc86a96d4d1f411f3cef130d97a3532386788e4b667054a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"835bf3eff9c469d21dc86a96d4d1f411f3cef130d97a3532386788e4b667054a","first_computed_at":"2026-05-18T03:56:36.002011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:36.002011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MrF4D3k+/ctGBTtHhClv7gRbmNkzO3UHSHBNzMHbS/GGnSrKHl1MW3OipyHgZrss3V/U6q15CaQpASaGrPZRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:36.002695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5dc072d0baf90aa92fcfc569b6454c3433383d0bb3cc7f7e6e8348bf9778fe3","sha256:a96e8e3d1b7be3013470daee4eb09ec76d61ada66800de5bad486120f0959e38"],"state_sha256":"02d32aaf44d87382031fc60179d549fe4673f75ee1c8596541835826bd9ee143"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Adf6D6gVdmhKhGMVIh42LhVjgLHxm5P/XojGDencP++J4w1cyUlA0yL7Dzphj3oFY3ys8kRxj7KpzhKJDuLnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:48:46.172603Z","bundle_sha256":"3127f9f571d782a7188a971c7ea91aa04eb9b5c3fa107320bf20c647bd67e9a0"}}