{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CU7KUQIPFBKNK2I3F3ENYYP5UD","short_pith_number":"pith:CU7KUQIP","canonical_record":{"source":{"id":"1701.06263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-01-23T04:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"98bca604148894a5030f0a3398d73a37b59601d86d06fc1bc8c74ec13de6e695","abstract_canon_sha256":"0718ef97825070d687286513bdb17f42c487d7ff82fa7b8b481060f8871805ce"},"schema_version":"1.0"},"canonical_sha256":"153eaa410f2854d5691b2ec8dc61fda0f1880ed4e81dbe2b017dbdb15977306e","source":{"kind":"arxiv","id":"1701.06263","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06263","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06263v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06263","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"CU7KUQIPFBKN","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CU7KUQIPFBKNK2I3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CU7KUQIP","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CU7KUQIPFBKNK2I3F3ENYYP5UD","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-01-23T04:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"98bca604148894a5030f0a3398d73a37b59601d86d06fc1bc8c74ec13de6e695","abstract_canon_sha256":"0718ef97825070d687286513bdb17f42c487d7ff82fa7b8b481060f8871805ce"},"schema_version":"1.0"},"canonical_sha256":"153eaa410f2854d5691b2ec8dc61fda0f1880ed4e81dbe2b017dbdb15977306e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:18.814078Z","signature_b64":"O/iIflvCCVGDsxl2UqgEbmH5ffu1zfMc1ttzhiYlK+BnMqxMXJ89osA3GmMPjjY8n4DV9CczvzzXUEc9WXmLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"153eaa410f2854d5691b2ec8dc61fda0f1880ed4e81dbe2b017dbdb15977306e","last_reissued_at":"2026-05-18T00:52:18.813443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:18.813443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06263","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":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+vW80CwqvFGjxOZbFZesN+2WG7BqAYqHrULi2e414UZhgARNhowCPVzvroomdayMhJcTmey3P1hVeA4/uOvHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:38:42.002082Z"},"content_sha256":"3572bfaa43df31c9315053d4b0b8ff7ba7dd6bceaa12d22f6d3d18dc8be9a055","schema_version":"1.0","event_id":"sha256:3572bfaa43df31c9315053d4b0b8ff7ba7dd6bceaa12d22f6d3d18dc8be9a055"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CU7KUQIPFBKNK2I3F3ENYYP5UD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonparametric Operator-Regularized Covariance Function Estimation for Functional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Raymond K. W. Wong, Xiaoke Zhang","submitted_at":"2017-01-23T04:14:59Z","abstract_excerpt":"In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper develops a new class of nonparametric covariance function estimators in terms of various spectral regularizations of an operator associated with a reproducing kernel Hilbert space. Despite their nonparametric nature, the covariance estimators are automatically positive semi-definite without any additional modification steps. An unconventional representer the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06263","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":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ibgJ205O5V1SORp2sRrVCi3H5OTyUaMALMLXuizlwQp2FpP+x4zZue000oAuLlTCuWu23zTb8w1KEBMVhWZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:38:42.002804Z"},"content_sha256":"497cad8a2742228fdd181ab1d124f636e96cc5f8590810994a3a35e22a4ce174","schema_version":"1.0","event_id":"sha256:497cad8a2742228fdd181ab1d124f636e96cc5f8590810994a3a35e22a4ce174"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/bundle.json","state_url":"https://pith.science/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/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":"2026-06-09T03:38:42Z","links":{"resolver":"https://pith.science/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD","bundle":"https://pith.science/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/bundle.json","state":"https://pith.science/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CU7KUQIPFBKNK2I3F3ENYYP5UD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CU7KUQIPFBKNK2I3F3ENYYP5UD","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":"0718ef97825070d687286513bdb17f42c487d7ff82fa7b8b481060f8871805ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-01-23T04:14:59Z","title_canon_sha256":"98bca604148894a5030f0a3398d73a37b59601d86d06fc1bc8c74ec13de6e695"},"schema_version":"1.0","source":{"id":"1701.06263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06263","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06263v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06263","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"CU7KUQIPFBKN","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CU7KUQIPFBKNK2I3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CU7KUQIP","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:497cad8a2742228fdd181ab1d124f636e96cc5f8590810994a3a35e22a4ce174","target":"graph","created_at":"2026-05-18T00:52:18Z","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":"In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper develops a new class of nonparametric covariance function estimators in terms of various spectral regularizations of an operator associated with a reproducing kernel Hilbert space. Despite their nonparametric nature, the covariance estimators are automatically positive semi-definite without any additional modification steps. An unconventional representer the","authors_text":"Raymond K. W. Wong, Xiaoke Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-01-23T04:14:59Z","title":"Nonparametric Operator-Regularized Covariance Function Estimation for Functional Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06263","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":"sha256:3572bfaa43df31c9315053d4b0b8ff7ba7dd6bceaa12d22f6d3d18dc8be9a055","target":"record","created_at":"2026-05-18T00:52:18Z","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":"0718ef97825070d687286513bdb17f42c487d7ff82fa7b8b481060f8871805ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-01-23T04:14:59Z","title_canon_sha256":"98bca604148894a5030f0a3398d73a37b59601d86d06fc1bc8c74ec13de6e695"},"schema_version":"1.0","source":{"id":"1701.06263","kind":"arxiv","version":1}},"canonical_sha256":"153eaa410f2854d5691b2ec8dc61fda0f1880ed4e81dbe2b017dbdb15977306e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"153eaa410f2854d5691b2ec8dc61fda0f1880ed4e81dbe2b017dbdb15977306e","first_computed_at":"2026-05-18T00:52:18.813443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:18.813443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/iIflvCCVGDsxl2UqgEbmH5ffu1zfMc1ttzhiYlK+BnMqxMXJ89osA3GmMPjjY8n4DV9CczvzzXUEc9WXmLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:18.814078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3572bfaa43df31c9315053d4b0b8ff7ba7dd6bceaa12d22f6d3d18dc8be9a055","sha256:497cad8a2742228fdd181ab1d124f636e96cc5f8590810994a3a35e22a4ce174"],"state_sha256":"765dcf4b3393f91995710f9db83e7fd90a5005a991c801a82b075a8f0243511c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTMAY9ICoaz4sjdL53dSYF6kozb5yI9i/IywtHCqEHDo6g2CcW6SLKaA2uEK6WW/1TcwP+G9TtowY9FM1+78BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:38:42.006824Z","bundle_sha256":"c7ae7e84f00fde888158f1e9e76b5077467506c9ba8d144aa8cd6800b1b06aed"}}