{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OLPB2SYADICZPRZSTGXLWBOGOM","short_pith_number":"pith:OLPB2SYA","canonical_record":{"source":{"id":"1102.1324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-02-07T14:41:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"97b0c4f8275feb88335d605a88ebc816f9ff455071969ad8ec3306e7d3514409","abstract_canon_sha256":"65627ac1fae54291b0f9862e79957c2ebb3a58ef7f0c38348a23622e96f7445a"},"schema_version":"1.0"},"canonical_sha256":"72de1d4b001a0597c73299aebb05c6731a0c24e7c0c44a6637a831b85c1e046f","source":{"kind":"arxiv","id":"1102.1324","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1324","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1324v1","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1324","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"OLPB2SYADICZ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OLPB2SYADICZPRZS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OLPB2SYA","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OLPB2SYADICZPRZSTGXLWBOGOM","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-02-07T14:41:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"97b0c4f8275feb88335d605a88ebc816f9ff455071969ad8ec3306e7d3514409","abstract_canon_sha256":"65627ac1fae54291b0f9862e79957c2ebb3a58ef7f0c38348a23622e96f7445a"},"schema_version":"1.0"},"canonical_sha256":"72de1d4b001a0597c73299aebb05c6731a0c24e7c0c44a6637a831b85c1e046f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:54.509023Z","signature_b64":"809t0GNfDp2/qngajHR7PDaNTcrx3uk9NCe4XQCi06hOXSZSJW6hT7nsf+aBbLFEuMAefsJFy1IpQLlZ58abCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72de1d4b001a0597c73299aebb05c6731a0c24e7c0c44a6637a831b85c1e046f","last_reissued_at":"2026-05-18T04:29:54.508381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:54.508381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1324","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":"2026-05-18T04:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ansAqqzOxa7DsJzUuMAw/0n7kmlcHG/UTwSQ2U+/zd5SnMeBNRaRHKd11SFJHQvte0Idzg8ct80HQZMI8q+sAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:19:31.436145Z"},"content_sha256":"209468a8ce6f1a82209d3a4bea908804bea0d44d3bf799365e1dc1d5fcb69011","schema_version":"1.0","event_id":"sha256:209468a8ce6f1a82209d3a4bea908804bea0d44d3bf799365e1dc1d5fcb69011"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OLPB2SYADICZPRZSTGXLWBOGOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refinement of Operator-valued Reproducing Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"cs.LG","authors_text":"Haizhang Zhang, Qinghui Zhang, Yuesheng Xu","submitted_at":"2011-02-07T14:41:30Z","abstract_excerpt":"This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occurs. Numerical simulations confirm that the established refinement kernel method is able to meet this need. Various characterizations are provided based on feature maps and vector-valued integral representat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1324","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":"2026-05-18T04:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uo1Mlm/+Lya63i0DrwmWDZenfEUMYj/wwjPEH4nVFvuqAxm0lToGnvs4OXLwQurImnewMmhOwXb++RBbRfbDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:19:31.436511Z"},"content_sha256":"77840794f28a9a441fb94790599e2b2e8dd698ff79857c6db23009a5746bb940","schema_version":"1.0","event_id":"sha256:77840794f28a9a441fb94790599e2b2e8dd698ff79857c6db23009a5746bb940"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLPB2SYADICZPRZSTGXLWBOGOM/bundle.json","state_url":"https://pith.science/pith/OLPB2SYADICZPRZSTGXLWBOGOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLPB2SYADICZPRZSTGXLWBOGOM/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":"2026-06-03T06:19:31Z","links":{"resolver":"https://pith.science/pith/OLPB2SYADICZPRZSTGXLWBOGOM","bundle":"https://pith.science/pith/OLPB2SYADICZPRZSTGXLWBOGOM/bundle.json","state":"https://pith.science/pith/OLPB2SYADICZPRZSTGXLWBOGOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLPB2SYADICZPRZSTGXLWBOGOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OLPB2SYADICZPRZSTGXLWBOGOM","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":"65627ac1fae54291b0f9862e79957c2ebb3a58ef7f0c38348a23622e96f7445a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-02-07T14:41:30Z","title_canon_sha256":"97b0c4f8275feb88335d605a88ebc816f9ff455071969ad8ec3306e7d3514409"},"schema_version":"1.0","source":{"id":"1102.1324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1324","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1324v1","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1324","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"OLPB2SYADICZ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OLPB2SYADICZPRZS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OLPB2SYA","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:77840794f28a9a441fb94790599e2b2e8dd698ff79857c6db23009a5746bb940","target":"graph","created_at":"2026-05-18T04:29:54Z","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 studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occurs. Numerical simulations confirm that the established refinement kernel method is able to meet this need. Various characterizations are provided based on feature maps and vector-valued integral representat","authors_text":"Haizhang Zhang, Qinghui Zhang, Yuesheng Xu","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-02-07T14:41:30Z","title":"Refinement of Operator-valued Reproducing Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1324","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":"sha256:209468a8ce6f1a82209d3a4bea908804bea0d44d3bf799365e1dc1d5fcb69011","target":"record","created_at":"2026-05-18T04:29:54Z","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":"65627ac1fae54291b0f9862e79957c2ebb3a58ef7f0c38348a23622e96f7445a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-02-07T14:41:30Z","title_canon_sha256":"97b0c4f8275feb88335d605a88ebc816f9ff455071969ad8ec3306e7d3514409"},"schema_version":"1.0","source":{"id":"1102.1324","kind":"arxiv","version":1}},"canonical_sha256":"72de1d4b001a0597c73299aebb05c6731a0c24e7c0c44a6637a831b85c1e046f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72de1d4b001a0597c73299aebb05c6731a0c24e7c0c44a6637a831b85c1e046f","first_computed_at":"2026-05-18T04:29:54.508381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:54.508381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"809t0GNfDp2/qngajHR7PDaNTcrx3uk9NCe4XQCi06hOXSZSJW6hT7nsf+aBbLFEuMAefsJFy1IpQLlZ58abCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:54.509023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:209468a8ce6f1a82209d3a4bea908804bea0d44d3bf799365e1dc1d5fcb69011","sha256:77840794f28a9a441fb94790599e2b2e8dd698ff79857c6db23009a5746bb940"],"state_sha256":"3943bbc940ea4c367f08a604a604914f27e72382b98aeeb4f77c2bc77e8f0ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fl055GasupS/qwAezbizEpoTmTqKc4WqR6aDGJ4kbezs7kRx8m10ct5q5VqpgZ8APWJA4eunyaJKB3QN6kHZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:19:31.438563Z","bundle_sha256":"b954dfa026de2ece325e28d06fda8e95992fc1a73d35db755fef86794bd55d2f"}}