{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:N7O32ZG6WAIM7QRD77HEZOMDZK","short_pith_number":"pith:N7O32ZG6","canonical_record":{"source":{"id":"2302.01178","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-02T15:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"f3bfbab428470e9ba8cdc6550ac95cee8c7b9a2360680511c51e3d086e1b115d","abstract_canon_sha256":"ea9fb04a1f01e19ca4c2c3d1f80197107372cdf66e3210de19829e1f5d9abc00"},"schema_version":"1.0"},"canonical_sha256":"6fddbd64deb010cfc223ffce4cb983ca8f150b5ee8c74c1417a6a62e60fc9f24","source":{"kind":"arxiv","id":"2302.01178","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.01178","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"2302.01178v3","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.01178","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"N7O32ZG6WAIM","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_16","alias_value":"N7O32ZG6WAIM7QRD","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_8","alias_value":"N7O32ZG6","created_at":"2026-07-05T07:19:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:N7O32ZG6WAIM7QRD77HEZOMDZK","target":"record","payload":{"canonical_record":{"source":{"id":"2302.01178","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-02T15:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"f3bfbab428470e9ba8cdc6550ac95cee8c7b9a2360680511c51e3d086e1b115d","abstract_canon_sha256":"ea9fb04a1f01e19ca4c2c3d1f80197107372cdf66e3210de19829e1f5d9abc00"},"schema_version":"1.0"},"canonical_sha256":"6fddbd64deb010cfc223ffce4cb983ca8f150b5ee8c74c1417a6a62e60fc9f24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:19:18.309593Z","signature_b64":"mddXo7UpnMScud/WlXJMVR0oax/8spxsfjaqedoke+3LAX04pC87YKyYLzzTwuCHPRAX+IDQFmzfPJN6lc/CAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fddbd64deb010cfc223ffce4cb983ca8f150b5ee8c74c1417a6a62e60fc9f24","last_reissued_at":"2026-07-05T07:19:18.308979Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:19:18.308979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.01178","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rX8eKN9gVYdGppL2Wiq8eLnrITotToLlMYRzI4sPoRnerA8SKAzVReRnp+JZzQzEm3GF38zo6wfUGRGagf23Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:42:49.233972Z"},"content_sha256":"7a1fdd00939ae187feaa7fee597a9a77c9f82cea68e24f82d41833de50f6733c","schema_version":"1.0","event_id":"sha256:7a1fdd00939ae187feaa7fee597a9a77c9f82cea68e24f82d41833de50f6733c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:N7O32ZG6WAIM7QRD77HEZOMDZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolutional Neural Operators for robust and accurate learning of PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bogdan Raoni\\'c, Emmanuel de B\\'ezenac, Francesca Bartolucci, Rima Alaifari, Roberto Molinaro, Siddhartha Mishra, Tim De Ryck, Tobias Rohner","submitted_at":"2023-02-02T15:54:45Z","abstract_excerpt":"Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01178","kind":"arxiv","version":3},"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/2302.01178/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":"2026-07-05T07:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlIdDmJ7BOK1qHn2JmnFImVnElDgf10FbV84rCu67oYPygsC4enAdbcFvyeZCkBAUcJKuSjs32/AJmbccDnuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:42:49.234776Z"},"content_sha256":"9401a3b98dac3048a2408de6bfb81f27807ff94d78ed100dc07a6ab87ee552f5","schema_version":"1.0","event_id":"sha256:9401a3b98dac3048a2408de6bfb81f27807ff94d78ed100dc07a6ab87ee552f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/bundle.json","state_url":"https://pith.science/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/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":"2026-08-16T01:42:49Z","links":{"resolver":"https://pith.science/pith/N7O32ZG6WAIM7QRD77HEZOMDZK","bundle":"https://pith.science/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/bundle.json","state":"https://pith.science/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7O32ZG6WAIM7QRD77HEZOMDZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:N7O32ZG6WAIM7QRD77HEZOMDZK","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":"ea9fb04a1f01e19ca4c2c3d1f80197107372cdf66e3210de19829e1f5d9abc00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-02T15:54:45Z","title_canon_sha256":"f3bfbab428470e9ba8cdc6550ac95cee8c7b9a2360680511c51e3d086e1b115d"},"schema_version":"1.0","source":{"id":"2302.01178","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.01178","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"2302.01178v3","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.01178","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"N7O32ZG6WAIM","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_16","alias_value":"N7O32ZG6WAIM7QRD","created_at":"2026-07-05T07:19:18Z"},{"alias_kind":"pith_short_8","alias_value":"N7O32ZG6","created_at":"2026-07-05T07:19:18Z"}],"graph_snapshots":[{"event_id":"sha256:9401a3b98dac3048a2408de6bfb81f27807ff94d78ed100dc07a6ab87ee552f5","target":"graph","created_at":"2026-07-05T07:19:18Z","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/2302.01178/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a com","authors_text":"Bogdan Raoni\\'c, Emmanuel de B\\'ezenac, Francesca Bartolucci, Rima Alaifari, Roberto Molinaro, Siddhartha Mishra, Tim De Ryck, Tobias Rohner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-02T15:54:45Z","title":"Convolutional Neural Operators for robust and accurate learning of PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01178","kind":"arxiv","version":3},"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":"sha256:7a1fdd00939ae187feaa7fee597a9a77c9f82cea68e24f82d41833de50f6733c","target":"record","created_at":"2026-07-05T07:19:18Z","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":"ea9fb04a1f01e19ca4c2c3d1f80197107372cdf66e3210de19829e1f5d9abc00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-02T15:54:45Z","title_canon_sha256":"f3bfbab428470e9ba8cdc6550ac95cee8c7b9a2360680511c51e3d086e1b115d"},"schema_version":"1.0","source":{"id":"2302.01178","kind":"arxiv","version":3}},"canonical_sha256":"6fddbd64deb010cfc223ffce4cb983ca8f150b5ee8c74c1417a6a62e60fc9f24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fddbd64deb010cfc223ffce4cb983ca8f150b5ee8c74c1417a6a62e60fc9f24","first_computed_at":"2026-07-05T07:19:18.308979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:19:18.308979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mddXo7UpnMScud/WlXJMVR0oax/8spxsfjaqedoke+3LAX04pC87YKyYLzzTwuCHPRAX+IDQFmzfPJN6lc/CAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:19:18.309593Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.01178","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a1fdd00939ae187feaa7fee597a9a77c9f82cea68e24f82d41833de50f6733c","sha256:9401a3b98dac3048a2408de6bfb81f27807ff94d78ed100dc07a6ab87ee552f5"],"state_sha256":"c094846b1a9128fa8efa3ceb52663557d2b1d259052c64b2b233df5077590c3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H3G2IxE1cXxnI/W18J8CCuj3YwXSn1cm9V4TxrMOegTizXJZalZtf31A20s6fGOZnfKlDcYc7IYrc6rPtfxxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:42:49.240884Z","bundle_sha256":"c377b4b777ff88be7a4a38516969a9a80c6108bce9cb951edc12e2e347899905"}}