{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CLR7E4OO53PPOYCG3NLLVIQYRE","short_pith_number":"pith:CLR7E4OO","canonical_record":{"source":{"id":"1901.10076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-01-29T02:44:08Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"98a1cbacdec630e55e5c810d948a8366a83014b9b4214c283c6c758aef093e82","abstract_canon_sha256":"72b237bb5cdd1df58479d22eae8dba8438451fdcceb6b2f8cdf065ca89391317"},"schema_version":"1.0"},"canonical_sha256":"12e3f271ceeedef76046db56baa218890fe42cf481856c6ef21a69b879c07ab0","source":{"kind":"arxiv","id":"1901.10076","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10076","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10076v2","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10076","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"pith_short_12","alias_value":"CLR7E4OO53PP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CLR7E4OO53PPOYCG","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CLR7E4OO","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CLR7E4OO53PPOYCG3NLLVIQYRE","target":"record","payload":{"canonical_record":{"source":{"id":"1901.10076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-01-29T02:44:08Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"98a1cbacdec630e55e5c810d948a8366a83014b9b4214c283c6c758aef093e82","abstract_canon_sha256":"72b237bb5cdd1df58479d22eae8dba8438451fdcceb6b2f8cdf065ca89391317"},"schema_version":"1.0"},"canonical_sha256":"12e3f271ceeedef76046db56baa218890fe42cf481856c6ef21a69b879c07ab0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:58.349429Z","signature_b64":"SsNyuNDZWcxLmxs8wYGjQw/w3jsfQ7q8KOyK760KC739lrOc4SjNVAvWCMVH0dwbxH8VHzbCUDNMjT7pEH0LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12e3f271ceeedef76046db56baa218890fe42cf481856c6ef21a69b879c07ab0","last_reissued_at":"2026-05-17T23:52:58.348744Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:58.348744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.10076","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVzJrqDeugjHr/byrtNVL04dxbdsfXezNtsAITYm16j5LGRyuDsliES46lDU/bh4eEzovx/FRXPq4r+lqD5LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:59:16.401955Z"},"content_sha256":"5b9615fa272554b21da18cb8b386b3039537ad133a2d83cddff428f87ffe3b3f","schema_version":"1.0","event_id":"sha256:5b9615fa272554b21da18cb8b386b3039537ad133a2d83cddff428f87ffe3b3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CLR7E4OO53PPOYCG3NLLVIQYRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Schatten--von Neumann Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","eess.SP"],"primary_cat":"stat.ML","authors_text":"Ivan Dokmani\\'c, Maarten de Hoop, Puoya Tabaghi","submitted_at":"2019-01-29T02:44:08Z","abstract_excerpt":"We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse problems. We address the question of sample complexity of learning Schatten-von Neumann operators and provide an upper bound on the number of measurements required for the empirical risk minimizer to generalize with arbitrary precision and probability, as a function of class parameter $p$. Our results give generalization guarantees for regression of infinit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10076","kind":"arxiv","version":2},"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":"2026-05-17T23:52:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+hSvzR/BBQJ1f2QJ+2PHWOrtyalfgNMSZqm5cGnLVW2QWJbO9TZPStZto6uqAodBLRDvEXeKZefEF43FbaGuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:59:16.402838Z"},"content_sha256":"0191afebdd993756a57220874d201e75861dba350c652d60dd8daa603d908351","schema_version":"1.0","event_id":"sha256:0191afebdd993756a57220874d201e75861dba350c652d60dd8daa603d908351"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/bundle.json","state_url":"https://pith.science/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/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":"2026-05-20T04:59:16Z","links":{"resolver":"https://pith.science/pith/CLR7E4OO53PPOYCG3NLLVIQYRE","bundle":"https://pith.science/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/bundle.json","state":"https://pith.science/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLR7E4OO53PPOYCG3NLLVIQYRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CLR7E4OO53PPOYCG3NLLVIQYRE","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":"72b237bb5cdd1df58479d22eae8dba8438451fdcceb6b2f8cdf065ca89391317","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-01-29T02:44:08Z","title_canon_sha256":"98a1cbacdec630e55e5c810d948a8366a83014b9b4214c283c6c758aef093e82"},"schema_version":"1.0","source":{"id":"1901.10076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10076","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10076v2","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10076","created_at":"2026-05-17T23:52:58Z"},{"alias_kind":"pith_short_12","alias_value":"CLR7E4OO53PP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CLR7E4OO53PPOYCG","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CLR7E4OO","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:0191afebdd993756a57220874d201e75861dba350c652d60dd8daa603d908351","target":"graph","created_at":"2026-05-17T23:52:58Z","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":"We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse problems. We address the question of sample complexity of learning Schatten-von Neumann operators and provide an upper bound on the number of measurements required for the empirical risk minimizer to generalize with arbitrary precision and probability, as a function of class parameter $p$. Our results give generalization guarantees for regression of infinit","authors_text":"Ivan Dokmani\\'c, Maarten de Hoop, Puoya Tabaghi","cross_cats":["cs.LG","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-01-29T02:44:08Z","title":"Learning Schatten--von Neumann Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10076","kind":"arxiv","version":2},"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":"sha256:5b9615fa272554b21da18cb8b386b3039537ad133a2d83cddff428f87ffe3b3f","target":"record","created_at":"2026-05-17T23:52:58Z","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":"72b237bb5cdd1df58479d22eae8dba8438451fdcceb6b2f8cdf065ca89391317","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-01-29T02:44:08Z","title_canon_sha256":"98a1cbacdec630e55e5c810d948a8366a83014b9b4214c283c6c758aef093e82"},"schema_version":"1.0","source":{"id":"1901.10076","kind":"arxiv","version":2}},"canonical_sha256":"12e3f271ceeedef76046db56baa218890fe42cf481856c6ef21a69b879c07ab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12e3f271ceeedef76046db56baa218890fe42cf481856c6ef21a69b879c07ab0","first_computed_at":"2026-05-17T23:52:58.348744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:58.348744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SsNyuNDZWcxLmxs8wYGjQw/w3jsfQ7q8KOyK760KC739lrOc4SjNVAvWCMVH0dwbxH8VHzbCUDNMjT7pEH0LAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:58.349429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b9615fa272554b21da18cb8b386b3039537ad133a2d83cddff428f87ffe3b3f","sha256:0191afebdd993756a57220874d201e75861dba350c652d60dd8daa603d908351"],"state_sha256":"4c3f153249d44b84a8bf1c258a939bb37137913863ecc61d56ab90e7827bd7c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OHwhbIcBh/h18x8cBebBwxoB1dQWCSNz+9pysTB9Ebz/FZbYrqs5QWne6XArZDQbIJntQxXN0hqwG4O/rc8ZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T04:59:16.407241Z","bundle_sha256":"8d90d7a5175e810c0d612eb80149c1757d6fa8f9967d2a86c332c0a73ee0bc1f"}}