{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:OWNJD5D46CVZHYNEFOP7PEY3CS","short_pith_number":"pith:OWNJD5D4","canonical_record":{"source":{"id":"2312.17348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-28T20:29:59Z","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"title_canon_sha256":"57f087c8c200b9c98e140d6798092354c03d64856c30380cc28b1aa30fe65db4","abstract_canon_sha256":"8568a73dcec68eb34579f818741dcb09587fc9b1189ef48e65151cc493e3e6d8"},"schema_version":"1.0"},"canonical_sha256":"759a91f47cf0ab93e1a42b9ff7931b1499c03b2be4443f7c099b7ce1e942b77d","source":{"kind":"arxiv","id":"2312.17348","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.17348","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"2312.17348v1","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.17348","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"OWNJD5D46CVZ","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"OWNJD5D46CVZHYNE","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"OWNJD5D4","created_at":"2026-07-05T07:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:OWNJD5D46CVZHYNEFOP7PEY3CS","target":"record","payload":{"canonical_record":{"source":{"id":"2312.17348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-28T20:29:59Z","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"title_canon_sha256":"57f087c8c200b9c98e140d6798092354c03d64856c30380cc28b1aa30fe65db4","abstract_canon_sha256":"8568a73dcec68eb34579f818741dcb09587fc9b1189ef48e65151cc493e3e6d8"},"schema_version":"1.0"},"canonical_sha256":"759a91f47cf0ab93e1a42b9ff7931b1499c03b2be4443f7c099b7ce1e942b77d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:28:49.759888Z","signature_b64":"RTHl7K/c/NhhifgbT3gbxJ1f6cGKxc8i+t/HBDWO+ZpOn2IJAqhzY4OEvRtPkQXL1D4WIUtVGOXUUIcVgfm6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"759a91f47cf0ab93e1a42b9ff7931b1499c03b2be4443f7c099b7ce1e942b77d","last_reissued_at":"2026-07-05T07:28:49.759364Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:28:49.759364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.17348","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":"2026-07-05T07:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEFzoTk1ccbyvJdmi0eUnvYKR6myBqetqNa9oDvQZKitldA/Phh7wP/tVkcm6NKBK1TMkKbr7EZVqOmaxsNaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:24:03.421958Z"},"content_sha256":"56a365388933d6bab8ed0c4d3c7df27b5dd1897a92df26a7ae8ad2302dc086fc","schema_version":"1.0","event_id":"sha256:56a365388933d6bab8ed0c4d3c7df27b5dd1897a92df26a7ae8ad2302dc086fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:OWNJD5D46CVZHYNEFOP7PEY3CS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A randomized algorithm to solve reduced rank operator regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Giacomo Turri, Massimiliano Pontil, Pietro Novelli, Vladimir Kostic","submitted_at":"2023-12-28T20:29:59Z","abstract_excerpt":"We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique to optimally learn a low-rank vector-valued function (i.e. an operator) between sampled data via regularized empirical risk minimization with rank constraints. We propose Gaussian sketching techniques both for the primal and dual optimization objectives, yielding Randomized Reduced Rank Regression (R4) estimators that are efficient and accurate. For each of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17348","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.17348/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ijyNXO4CUWxU3Qw0rfUPNuWo5P5211gIJA8+ULn95e+UVQEq7SSCnZPuPCWP5ZGvGO+Cxrx72/g1cmPlkmIvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:24:03.422368Z"},"content_sha256":"e9b641e2674d9e346d55544c9206f6a290d069703751e99c4b23a9f3c16ec217","schema_version":"1.0","event_id":"sha256:e9b641e2674d9e346d55544c9206f6a290d069703751e99c4b23a9f3c16ec217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/bundle.json","state_url":"https://pith.science/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/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":"2026-07-09T04:24:03Z","links":{"resolver":"https://pith.science/pith/OWNJD5D46CVZHYNEFOP7PEY3CS","bundle":"https://pith.science/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/bundle.json","state":"https://pith.science/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWNJD5D46CVZHYNEFOP7PEY3CS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:OWNJD5D46CVZHYNEFOP7PEY3CS","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":"8568a73dcec68eb34579f818741dcb09587fc9b1189ef48e65151cc493e3e6d8","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-28T20:29:59Z","title_canon_sha256":"57f087c8c200b9c98e140d6798092354c03d64856c30380cc28b1aa30fe65db4"},"schema_version":"1.0","source":{"id":"2312.17348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.17348","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"2312.17348v1","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.17348","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"OWNJD5D46CVZ","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"OWNJD5D46CVZHYNE","created_at":"2026-07-05T07:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"OWNJD5D4","created_at":"2026-07-05T07:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:e9b641e2674d9e346d55544c9206f6a290d069703751e99c4b23a9f3c16ec217","target":"graph","created_at":"2026-07-05T07:28:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.17348/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique to optimally learn a low-rank vector-valued function (i.e. an operator) between sampled data via regularized empirical risk minimization with rank constraints. We propose Gaussian sketching techniques both for the primal and dual optimization objectives, yielding Randomized Reduced Rank Regression (R4) estimators that are efficient and accurate. For each of ","authors_text":"Giacomo Turri, Massimiliano Pontil, Pietro Novelli, Vladimir Kostic","cross_cats":["cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-28T20:29:59Z","title":"A randomized algorithm to solve reduced rank operator regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17348","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":"sha256:56a365388933d6bab8ed0c4d3c7df27b5dd1897a92df26a7ae8ad2302dc086fc","target":"record","created_at":"2026-07-05T07:28:49Z","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":"8568a73dcec68eb34579f818741dcb09587fc9b1189ef48e65151cc493e3e6d8","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-28T20:29:59Z","title_canon_sha256":"57f087c8c200b9c98e140d6798092354c03d64856c30380cc28b1aa30fe65db4"},"schema_version":"1.0","source":{"id":"2312.17348","kind":"arxiv","version":1}},"canonical_sha256":"759a91f47cf0ab93e1a42b9ff7931b1499c03b2be4443f7c099b7ce1e942b77d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"759a91f47cf0ab93e1a42b9ff7931b1499c03b2be4443f7c099b7ce1e942b77d","first_computed_at":"2026-07-05T07:28:49.759364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:28:49.759364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RTHl7K/c/NhhifgbT3gbxJ1f6cGKxc8i+t/HBDWO+ZpOn2IJAqhzY4OEvRtPkQXL1D4WIUtVGOXUUIcVgfm6Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T07:28:49.759888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.17348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56a365388933d6bab8ed0c4d3c7df27b5dd1897a92df26a7ae8ad2302dc086fc","sha256:e9b641e2674d9e346d55544c9206f6a290d069703751e99c4b23a9f3c16ec217"],"state_sha256":"ae79992291659681e4151e825a959db516fd466263ae83303e13c5e1de8295f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehjnNni0YwfGXzKTGqJYbcNcgknc0Q3rG5OCHGV9AuUF//FMV4YVrl9T3+tKJNOe+5gvTFAEFjGUqqDNLbmTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T04:24:03.424573Z","bundle_sha256":"45ee8e8a5e3f3583494f1aacc1e72ee305800a01dbf98b8e1d4f2beb6ea20508"}}