{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NB5YZB3PJESXMPX6A7IQSWE6QM","short_pith_number":"pith:NB5YZB3P","canonical_record":{"source":{"id":"1610.09915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-31T13:36:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1db4175e4eca1a786d89db63eb182fe9124717e433085a01baeaf57f4db2a1db","abstract_canon_sha256":"b6c408a7c449c64f4aaeba1e5563c1ce3de3453e4c82bc34e79e845656d93208"},"schema_version":"1.0"},"canonical_sha256":"687b8c876f4925763efe07d109589e831005957eeaa735b2bd4e71f8ac0e6c6d","source":{"kind":"arxiv","id":"1610.09915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09915","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09915v1","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09915","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"NB5YZB3PJESX","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NB5YZB3PJESXMPX6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NB5YZB3P","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NB5YZB3PJESXMPX6A7IQSWE6QM","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-31T13:36:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1db4175e4eca1a786d89db63eb182fe9124717e433085a01baeaf57f4db2a1db","abstract_canon_sha256":"b6c408a7c449c64f4aaeba1e5563c1ce3de3453e4c82bc34e79e845656d93208"},"schema_version":"1.0"},"canonical_sha256":"687b8c876f4925763efe07d109589e831005957eeaa735b2bd4e71f8ac0e6c6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:21.172642Z","signature_b64":"CnvwxrB2xTyLmu3mKGA26QdpZ66nMIavYjQZ8+oAT0DiH+CXDSG89yl46ZeOwGuK1Ttb+RwcFx+n3ae6wItBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"687b8c876f4925763efe07d109589e831005957eeaa735b2bd4e71f8ac0e6c6d","last_reissued_at":"2026-05-18T00:22:21.172145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:21.172145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09915","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":"2026-05-18T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEbM7dkN+CHQxJJuGhy71Ppu8AtnFLLp0+QaJ2Jy0+VZQ1Gol32RMFT61wAFaKwTYibiS/VhqrDbpzOtksVWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:28.260500Z"},"content_sha256":"e9d9adb79675b0e847f66bdb6ae400ad7cb75998740c8c35c1ff0e7f8b521a67","schema_version":"1.0","event_id":"sha256:e9d9adb79675b0e847f66bdb6ae400ad7cb75998740c8c35c1ff0e7f8b521a67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NB5YZB3PJESXMPX6A7IQSWE6QM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex-Valued Kernel Methods for Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Fernando P\\'erez-Cruz, Irene Santos Vel\\'azquez, Juan Jos\\'e Murillo-Fuentes, Rafael Boloix-Tortosa","submitted_at":"2016-10-31T13:36:53Z","abstract_excerpt":"Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo kernel, is needed to learn any function in complex-valued fields. Accordingly, we derive a novel RKHS to include it, the widely RKHS (WRKHS). When the pseudo-kernel cancels, WRKHS reduces to complex-valued RKHS of previous approaches. We address the kernel and pseudo-kernel design, paying attention to the kernel and the pseudo-kernel being complex-valued. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09915","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":"2026-05-18T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTph8Y7syIchQipf/B1PiU2CqOtrzBBGCXIZ55yDB/BSGF8V0tJoJzP/+LNl8vxbjU6uIh5Uz+wCVjTFa1HPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:28.260853Z"},"content_sha256":"7853854d94d96ff4501a2022da5c8b73c0bf7ab20f9f3f09cbe99ae92f2d2d86","schema_version":"1.0","event_id":"sha256:7853854d94d96ff4501a2022da5c8b73c0bf7ab20f9f3f09cbe99ae92f2d2d86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/bundle.json","state_url":"https://pith.science/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/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":"2026-06-02T22:19:28Z","links":{"resolver":"https://pith.science/pith/NB5YZB3PJESXMPX6A7IQSWE6QM","bundle":"https://pith.science/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/bundle.json","state":"https://pith.science/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NB5YZB3PJESXMPX6A7IQSWE6QM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NB5YZB3PJESXMPX6A7IQSWE6QM","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":"b6c408a7c449c64f4aaeba1e5563c1ce3de3453e4c82bc34e79e845656d93208","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-31T13:36:53Z","title_canon_sha256":"1db4175e4eca1a786d89db63eb182fe9124717e433085a01baeaf57f4db2a1db"},"schema_version":"1.0","source":{"id":"1610.09915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09915","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09915v1","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09915","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"NB5YZB3PJESX","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NB5YZB3PJESXMPX6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NB5YZB3P","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:7853854d94d96ff4501a2022da5c8b73c0bf7ab20f9f3f09cbe99ae92f2d2d86","target":"graph","created_at":"2026-05-18T00:22:21Z","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":"Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo kernel, is needed to learn any function in complex-valued fields. Accordingly, we derive a novel RKHS to include it, the widely RKHS (WRKHS). When the pseudo-kernel cancels, WRKHS reduces to complex-valued RKHS of previous approaches. We address the kernel and pseudo-kernel design, paying attention to the kernel and the pseudo-kernel being complex-valued. In ","authors_text":"Fernando P\\'erez-Cruz, Irene Santos Vel\\'azquez, Juan Jos\\'e Murillo-Fuentes, Rafael Boloix-Tortosa","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-31T13:36:53Z","title":"Complex-Valued Kernel Methods for Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09915","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:e9d9adb79675b0e847f66bdb6ae400ad7cb75998740c8c35c1ff0e7f8b521a67","target":"record","created_at":"2026-05-18T00:22:21Z","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":"b6c408a7c449c64f4aaeba1e5563c1ce3de3453e4c82bc34e79e845656d93208","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-31T13:36:53Z","title_canon_sha256":"1db4175e4eca1a786d89db63eb182fe9124717e433085a01baeaf57f4db2a1db"},"schema_version":"1.0","source":{"id":"1610.09915","kind":"arxiv","version":1}},"canonical_sha256":"687b8c876f4925763efe07d109589e831005957eeaa735b2bd4e71f8ac0e6c6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"687b8c876f4925763efe07d109589e831005957eeaa735b2bd4e71f8ac0e6c6d","first_computed_at":"2026-05-18T00:22:21.172145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:21.172145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CnvwxrB2xTyLmu3mKGA26QdpZ66nMIavYjQZ8+oAT0DiH+CXDSG89yl46ZeOwGuK1Ttb+RwcFx+n3ae6wItBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:21.172642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d9adb79675b0e847f66bdb6ae400ad7cb75998740c8c35c1ff0e7f8b521a67","sha256:7853854d94d96ff4501a2022da5c8b73c0bf7ab20f9f3f09cbe99ae92f2d2d86"],"state_sha256":"2980a262b9baa7ab238de24e003ce5b328e9e97bde2430072491ba2c1da14b21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOYfaF0q5MxccEQC2/HsfZzJZ9sWdG9tGwmmK2qyRjVc76v4XCSdkCMhQhhrRpmK/NbQwwPyXH2Wy1MF4i88Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:19:28.262870Z","bundle_sha256":"5843ce272fd4acc2c5cbf2cb1b7a24e35eb0ad76c325d14c1ba548b664f3ba98"}}