{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:FCVG26OTFWZTXJPV2ZS27RL2KV","short_pith_number":"pith:FCVG26OT","schema_version":"1.0","canonical_sha256":"28aa6d79d32db33ba5f5d665afc57a5579aff667614138d77ffefd5c5f433507","source":{"kind":"arxiv","id":"2306.03838","version":1},"attestation_state":"computed","paper":{"title":"Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.ao-ph","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Anima Anandkumar, Boris Bonev, Christian Hundt, Jaideep Pathak, Karthik Kashinath, Maximilian Baust, Thorsten Kurth","submitted_at":"2023-06-06T16:27:17Z","abstract_excerpt":"Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they "},"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":"2306.03838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-06-06T16:27:17Z","cross_cats_sorted":["cs.NA","math.NA","physics.ao-ph","physics.comp-ph"],"title_canon_sha256":"bdfa6badfff8965b6f8ab749759d4aa2fa314aca223b94b16b7cdf02f1d08637","abstract_canon_sha256":"358d5d554d26457ea693b2157fa6411d58a7cddb7194b3ac4ba9b2b41835728b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:18:02.762532Z","signature_b64":"Zdoh420PXYPgF7mQBDBOl42IvH8S0eGRU0eVL/U1fmdB0A8LIGZAicRnYAsjjcAoYcjdNMLkP7ivSlfIUDg8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28aa6d79d32db33ba5f5d665afc57a5579aff667614138d77ffefd5c5f433507","last_reissued_at":"2026-07-05T06:18:02.762157Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:18:02.762157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.ao-ph","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Anima Anandkumar, Boris Bonev, Christian Hundt, Jaideep Pathak, Karthik Kashinath, Maximilian Baust, Thorsten Kurth","submitted_at":"2023-06-06T16:27:17Z","abstract_excerpt":"Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03838","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/2306.03838/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":"2306.03838","created_at":"2026-07-05T06:18:02.762213+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.03838v1","created_at":"2026-07-05T06:18:02.762213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.03838","created_at":"2026-07-05T06:18:02.762213+00:00"},{"alias_kind":"pith_short_12","alias_value":"FCVG26OTFWZT","created_at":"2026-07-05T06:18:02.762213+00:00"},{"alias_kind":"pith_short_16","alias_value":"FCVG26OTFWZTXJPV","created_at":"2026-07-05T06:18:02.762213+00:00"},{"alias_kind":"pith_short_8","alias_value":"FCVG26OT","created_at":"2026-07-05T06:18:02.762213+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.24658","citing_title":"WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2606.07928","citing_title":"Disentangling the effects of sea surface temperature and CO$_2$ in global machine learned weather-climate emulators","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2511.22112","citing_title":"Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2512.08614","citing_title":"PyMieDiff: A differentiable Mie scattering library","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2602.16090","citing_title":"Examining Fast Radiatively Driven Responses Using Machine-Learning Weather Emulators","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09041","citing_title":"U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV","json":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV.json","graph_json":"https://pith.science/api/pith-number/FCVG26OTFWZTXJPV2ZS27RL2KV/graph.json","events_json":"https://pith.science/api/pith-number/FCVG26OTFWZTXJPV2ZS27RL2KV/events.json","paper":"https://pith.science/paper/FCVG26OT"},"agent_actions":{"view_html":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV","download_json":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV.json","view_paper":"https://pith.science/paper/FCVG26OT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.03838&json=true","fetch_graph":"https://pith.science/api/pith-number/FCVG26OTFWZTXJPV2ZS27RL2KV/graph.json","fetch_events":"https://pith.science/api/pith-number/FCVG26OTFWZTXJPV2ZS27RL2KV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV/action/storage_attestation","attest_author":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV/action/author_attestation","sign_citation":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV/action/citation_signature","submit_replication":"https://pith.science/pith/FCVG26OTFWZTXJPV2ZS27RL2KV/action/replication_record"}},"created_at":"2026-07-05T06:18:02.762213+00:00","updated_at":"2026-07-05T06:18:02.762213+00:00"}