{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZGKT3IHCUPKXO2WBB2UOKARXFI","short_pith_number":"pith:ZGKT3IHC","canonical_record":{"source":{"id":"2504.03503","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-04-04T14:58:45Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0d89fcebfcfc849cc79c51b01de3a5a89aa1fe2057506f8b03532dd361c30805","abstract_canon_sha256":"db3dcb2c7394289aabadd11fd6c7ceff9307f784549236075f521b57e13c91d6"},"schema_version":"1.0"},"canonical_sha256":"c9953da0e2a3d5776ac10ea8e502372a3dc1d92dba0e93ce24b4a30496b56553","source":{"kind":"arxiv","id":"2504.03503","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.03503","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"2504.03503v1","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.03503","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZGKT3IHCUPKX","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZGKT3IHCUPKXO2WB","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZGKT3IHC","created_at":"2026-07-05T10:44:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZGKT3IHCUPKXO2WBB2UOKARXFI","target":"record","payload":{"canonical_record":{"source":{"id":"2504.03503","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-04-04T14:58:45Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0d89fcebfcfc849cc79c51b01de3a5a89aa1fe2057506f8b03532dd361c30805","abstract_canon_sha256":"db3dcb2c7394289aabadd11fd6c7ceff9307f784549236075f521b57e13c91d6"},"schema_version":"1.0"},"canonical_sha256":"c9953da0e2a3d5776ac10ea8e502372a3dc1d92dba0e93ce24b4a30496b56553","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:33.087074Z","signature_b64":"16IpO6qGRLbCblQTXhciv4OVM+o6IrOPJbiLYtap2L13ZyGl7jBJBba9h7JgRly2sRjem24n5RtYR3KXNmrECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9953da0e2a3d5776ac10ea8e502372a3dc1d92dba0e93ce24b4a30496b56553","last_reissued_at":"2026-07-05T10:44:33.086624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:33.086624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.03503","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":"2026-07-05T10:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSqLys3r8wv3w8N8kAMGx6CHiLZRlPk69q8j+wrcONt/EnCou+XmqntrGBHS7DraZwSr2K4X3LnLET2frI5dCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T06:31:10.045803Z"},"content_sha256":"caf7cde729f73996df287b26f1e6c3fe27b99784120dc465ae9bb764cde7007c","schema_version":"1.0","event_id":"sha256:caf7cde729f73996df287b26f1e6c3fe27b99784120dc465ae9bb764cde7007c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZGKT3IHCUPKXO2WBB2UOKARXFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator Learning: A Statistical Perspective","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ambuj Tewari, Unique Subedi","submitted_at":"2025-04-04T14:58:45Z","abstract_excerpt":"Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.03503","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/2504.03503/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":"2026-07-05T10:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EyEyBmTEDveTX3eIGTPIYE1lmglvjkOTuKyiLb7gTRJyaAxWyY3VkhjaL/8tZ+pA4jevHe1l8ZOm2CcvIh9mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T06:31:10.046341Z"},"content_sha256":"c2e7722464a039be939a2df78056f44313607a4a5d1174eed3d3930fe0f5eb1a","schema_version":"1.0","event_id":"sha256:c2e7722464a039be939a2df78056f44313607a4a5d1174eed3d3930fe0f5eb1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/bundle.json","state_url":"https://pith.science/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/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":"2026-08-07T06:31:10Z","links":{"resolver":"https://pith.science/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI","bundle":"https://pith.science/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/bundle.json","state":"https://pith.science/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGKT3IHCUPKXO2WBB2UOKARXFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZGKT3IHCUPKXO2WBB2UOKARXFI","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":"db3dcb2c7394289aabadd11fd6c7ceff9307f784549236075f521b57e13c91d6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-04-04T14:58:45Z","title_canon_sha256":"0d89fcebfcfc849cc79c51b01de3a5a89aa1fe2057506f8b03532dd361c30805"},"schema_version":"1.0","source":{"id":"2504.03503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.03503","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"2504.03503v1","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.03503","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZGKT3IHCUPKX","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZGKT3IHCUPKXO2WB","created_at":"2026-07-05T10:44:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZGKT3IHC","created_at":"2026-07-05T10:44:33Z"}],"graph_snapshots":[{"event_id":"sha256:c2e7722464a039be939a2df78056f44313607a4a5d1174eed3d3930fe0f5eb1a","target":"graph","created_at":"2026-07-05T10:44:33Z","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/2504.03503/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the fie","authors_text":"Ambuj Tewari, Unique Subedi","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-04-04T14:58:45Z","title":"Operator Learning: A Statistical Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.03503","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:caf7cde729f73996df287b26f1e6c3fe27b99784120dc465ae9bb764cde7007c","target":"record","created_at":"2026-07-05T10:44:33Z","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":"db3dcb2c7394289aabadd11fd6c7ceff9307f784549236075f521b57e13c91d6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-04-04T14:58:45Z","title_canon_sha256":"0d89fcebfcfc849cc79c51b01de3a5a89aa1fe2057506f8b03532dd361c30805"},"schema_version":"1.0","source":{"id":"2504.03503","kind":"arxiv","version":1}},"canonical_sha256":"c9953da0e2a3d5776ac10ea8e502372a3dc1d92dba0e93ce24b4a30496b56553","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9953da0e2a3d5776ac10ea8e502372a3dc1d92dba0e93ce24b4a30496b56553","first_computed_at":"2026-07-05T10:44:33.086624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:44:33.086624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"16IpO6qGRLbCblQTXhciv4OVM+o6IrOPJbiLYtap2L13ZyGl7jBJBba9h7JgRly2sRjem24n5RtYR3KXNmrECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:44:33.087074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.03503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caf7cde729f73996df287b26f1e6c3fe27b99784120dc465ae9bb764cde7007c","sha256:c2e7722464a039be939a2df78056f44313607a4a5d1174eed3d3930fe0f5eb1a"],"state_sha256":"1de3721668412f287b0e83d0185dd404e31ef33d34095d3d58a4ae1add05017c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cVYuInnCqGEA3C5t1fk1xdeYm6QATleu7M8X9MnyTtURE/pseH9npclxa/EIisJaRiIdS9YIJjtZcOhVA3StCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T06:31:10.051873Z","bundle_sha256":"3de2f0be819f55c28cf9a99606a0ceb5700415202ea93aa5dd42dc21cae90820"}}