{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PY5VZ5XNDTIZGNB33DTLD3WRSF","short_pith_number":"pith:PY5VZ5XN","schema_version":"1.0","canonical_sha256":"7e3b5cf6ed1cd193343bd8e6b1eed1914c3156c62f8cc56dd7b0a13906eb842c","source":{"kind":"arxiv","id":"2603.00819","version":2},"attestation_state":"computed","paper":{"title":"A short tour of operator learning theory: Convergence rates, statistical limits, and open questions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Nicholas H. Nelsen, Nicola Rares Franco, Simone Brugiapaglia","submitted_at":"2026-02-28T21:36:40Z","abstract_excerpt":"This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and neural network approximations. Next, it illustrates fundamental performance limits in terms of sample size by adopting a minimax perspective and considering various notions of regularity beyond holomorphy. The paper ends with a discussion on the interplay between these two perspectives and related open questions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.00819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-02-28T21:36:40Z","cross_cats_sorted":["cs.LG","cs.NA","math.ST","stat.TH"],"title_canon_sha256":"18e3edef10ccaa95719e5ea9c299599ce7b836c5018e71b355b21732aec08878","abstract_canon_sha256":"a808e2da85f114a94c47494cab9fd0bb1e8421ee19fb59e809b398bb3f265786"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T00:15:52.936914Z","signature_b64":"VFCYTIgCfIf22aXMie7Y9u7E6zYyX0NIn5Tjzzn51mAElCQcA8LrdCBRIrpLKRgFjzrl0lxMLglXd4uVRIklAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e3b5cf6ed1cd193343bd8e6b1eed1914c3156c62f8cc56dd7b0a13906eb842c","last_reissued_at":"2026-07-07T00:15:52.936012Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T00:15:52.936012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short tour of operator learning theory: Convergence rates, statistical limits, and open questions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Nicholas H. Nelsen, Nicola Rares Franco, Simone Brugiapaglia","submitted_at":"2026-02-28T21:36:40Z","abstract_excerpt":"This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and neural network approximations. Next, it illustrates fundamental performance limits in terms of sample size by adopting a minimax perspective and considering various notions of regularity beyond holomorphy. The paper ends with a discussion on the interplay between these two perspectives and related open questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.00819","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.00819/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.00819","created_at":"2026-07-07T00:15:52.936130+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.00819v2","created_at":"2026-07-07T00:15:52.936130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.00819","created_at":"2026-07-07T00:15:52.936130+00:00"},{"alias_kind":"pith_short_12","alias_value":"PY5VZ5XNDTIZ","created_at":"2026-07-07T00:15:52.936130+00:00"},{"alias_kind":"pith_short_16","alias_value":"PY5VZ5XNDTIZGNB3","created_at":"2026-07-07T00:15:52.936130+00:00"},{"alias_kind":"pith_short_8","alias_value":"PY5VZ5XN","created_at":"2026-07-07T00:15:52.936130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.06873","citing_title":"One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2605.06873","citing_title":"One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF","json":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF.json","graph_json":"https://pith.science/api/pith-number/PY5VZ5XNDTIZGNB33DTLD3WRSF/graph.json","events_json":"https://pith.science/api/pith-number/PY5VZ5XNDTIZGNB33DTLD3WRSF/events.json","paper":"https://pith.science/paper/PY5VZ5XN"},"agent_actions":{"view_html":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF","download_json":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF.json","view_paper":"https://pith.science/paper/PY5VZ5XN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.00819&json=true","fetch_graph":"https://pith.science/api/pith-number/PY5VZ5XNDTIZGNB33DTLD3WRSF/graph.json","fetch_events":"https://pith.science/api/pith-number/PY5VZ5XNDTIZGNB33DTLD3WRSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF/action/storage_attestation","attest_author":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF/action/author_attestation","sign_citation":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF/action/citation_signature","submit_replication":"https://pith.science/pith/PY5VZ5XNDTIZGNB33DTLD3WRSF/action/replication_record"}},"created_at":"2026-07-07T00:15:52.936130+00:00","updated_at":"2026-07-07T00:15:52.936130+00:00"}