{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DMWMJRRKRX4KAIYQAJYCGWEFYP","short_pith_number":"pith:DMWMJRRK","canonical_record":{"source":{"id":"1809.07347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-19T18:00:51Z","cross_cats_sorted":["cs.AI","eess.SP","math.OC","stat.ML"],"title_canon_sha256":"4b5eb72c243dae21133147c0572ad0cd5b5f8a7c81d4fb6a5f6ed580eef52e36","abstract_canon_sha256":"cc95f483a1e41c55d5f118e0f4fdc667ad20ed0d9557e967e96e00db29f326ae"},"schema_version":"1.0"},"canonical_sha256":"1b2cc4c62a8df8a023100270235885c3c92d283a51e07e5e58c50317a845a4ad","source":{"kind":"arxiv","id":"1809.07347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07347","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07347v1","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07347","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"pith_short_12","alias_value":"DMWMJRRKRX4K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMWMJRRKRX4KAIYQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMWMJRRK","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DMWMJRRKRX4KAIYQAJYCGWEFYP","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-19T18:00:51Z","cross_cats_sorted":["cs.AI","eess.SP","math.OC","stat.ML"],"title_canon_sha256":"4b5eb72c243dae21133147c0572ad0cd5b5f8a7c81d4fb6a5f6ed580eef52e36","abstract_canon_sha256":"cc95f483a1e41c55d5f118e0f4fdc667ad20ed0d9557e967e96e00db29f326ae"},"schema_version":"1.0"},"canonical_sha256":"1b2cc4c62a8df8a023100270235885c3c92d283a51e07e5e58c50317a845a4ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:18.744343Z","signature_b64":"pSCOAwOjsvsd3PihEPkvVeNqWmLx2C1OCsMKLYeU6EGinSikS9sCsy3f0jTkYgKc+gad6o3s6GL7tVkTA29FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2cc4c62a8df8a023100270235885c3c92d283a51e07e5e58c50317a845a4ad","last_reissued_at":"2026-05-18T00:05:18.743734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:18.743734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07347","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":"2026-05-18T00:05:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMjD0kclfi99HQ4Z/fdOOsG9eyReR5J9KZT7Sdj+Ijnufrv5ODEdXuMozpWBt3OMqGuxzFLUWMel7KazpVJ9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:08:55.034360Z"},"content_sha256":"2092799e5d32eb96e39316e2936816e63e26e21cb3978fa61e92870c4058d451","schema_version":"1.0","event_id":"sha256:2092799e5d32eb96e39316e2936816e63e26e21cb3978fa61e92870c4058d451"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DMWMJRRKRX4KAIYQAJYCGWEFYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generalized Representer Theorem for Hilbert Space - Valued Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","eess.SP","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Colin Jones, Sanket Diwale","submitted_at":"2018-09-19T18:00:51Z","abstract_excerpt":"The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence in various machine learning algorithms like generalized least squares, support vector machines, Gaussian process regression and kernel based deep neural networks to name a few. Due to the more general structure of the underlying variational problems, the theory is also relevant to other application areas like optimal control, signal processing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07347","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":"2026-05-18T00:05:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTdLdztRZHeaiVkIxyyKld0f9MLC1LGMniyYkCFWYjr9nwnPul5U2VdKh04qnH9watev5QjwPu3SkA9HTKsFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:08:55.035110Z"},"content_sha256":"f4f39e7b26d8020e280b3ae005759ff38039be57166cfd2f7d41aac1837340ac","schema_version":"1.0","event_id":"sha256:f4f39e7b26d8020e280b3ae005759ff38039be57166cfd2f7d41aac1837340ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/bundle.json","state_url":"https://pith.science/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/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":"2026-06-08T06:08:55Z","links":{"resolver":"https://pith.science/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP","bundle":"https://pith.science/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/bundle.json","state":"https://pith.science/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMWMJRRKRX4KAIYQAJYCGWEFYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DMWMJRRKRX4KAIYQAJYCGWEFYP","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":"cc95f483a1e41c55d5f118e0f4fdc667ad20ed0d9557e967e96e00db29f326ae","cross_cats_sorted":["cs.AI","eess.SP","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-19T18:00:51Z","title_canon_sha256":"4b5eb72c243dae21133147c0572ad0cd5b5f8a7c81d4fb6a5f6ed580eef52e36"},"schema_version":"1.0","source":{"id":"1809.07347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07347","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07347v1","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07347","created_at":"2026-05-18T00:05:18Z"},{"alias_kind":"pith_short_12","alias_value":"DMWMJRRKRX4K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMWMJRRKRX4KAIYQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMWMJRRK","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:f4f39e7b26d8020e280b3ae005759ff38039be57166cfd2f7d41aac1837340ac","target":"graph","created_at":"2026-05-18T00:05:18Z","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":"The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence in various machine learning algorithms like generalized least squares, support vector machines, Gaussian process regression and kernel based deep neural networks to name a few. Due to the more general structure of the underlying variational problems, the theory is also relevant to other application areas like optimal control, signal processing ","authors_text":"Colin Jones, Sanket Diwale","cross_cats":["cs.AI","eess.SP","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-19T18:00:51Z","title":"A Generalized Representer Theorem for Hilbert Space - Valued Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07347","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":"sha256:2092799e5d32eb96e39316e2936816e63e26e21cb3978fa61e92870c4058d451","target":"record","created_at":"2026-05-18T00:05:18Z","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":"cc95f483a1e41c55d5f118e0f4fdc667ad20ed0d9557e967e96e00db29f326ae","cross_cats_sorted":["cs.AI","eess.SP","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-19T18:00:51Z","title_canon_sha256":"4b5eb72c243dae21133147c0572ad0cd5b5f8a7c81d4fb6a5f6ed580eef52e36"},"schema_version":"1.0","source":{"id":"1809.07347","kind":"arxiv","version":1}},"canonical_sha256":"1b2cc4c62a8df8a023100270235885c3c92d283a51e07e5e58c50317a845a4ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2cc4c62a8df8a023100270235885c3c92d283a51e07e5e58c50317a845a4ad","first_computed_at":"2026-05-18T00:05:18.743734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:18.743734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSCOAwOjsvsd3PihEPkvVeNqWmLx2C1OCsMKLYeU6EGinSikS9sCsy3f0jTkYgKc+gad6o3s6GL7tVkTA29FAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:18.744343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2092799e5d32eb96e39316e2936816e63e26e21cb3978fa61e92870c4058d451","sha256:f4f39e7b26d8020e280b3ae005759ff38039be57166cfd2f7d41aac1837340ac"],"state_sha256":"56f242362f406472e0fbd012158821686e7a3765abc84b838d7fb53db54beb2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhnl5dfqiDLnKWJkV2muJTzWQPpARDp3McMO1+79Qo9FESOPmCpW9HJBQwQoWMpmQCMApV/r0RlZ68wzwkT/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:08:55.039092Z","bundle_sha256":"db6a67e4941d098197976ff8944353799c2d947b2e9e128a0f909cbe71745e3a"}}