{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SYHD4KBTJMTP55XEIBFMWF4QDP","short_pith_number":"pith:SYHD4KBT","canonical_record":{"source":{"id":"2606.03469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T10:46:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"aef79694717fd3b598e8b65af3cc98ef5c8fbba4aed74b41f61a466156416efa","abstract_canon_sha256":"72f2941dbd70d24a8a2cf555944c76212fe32ae04711795e42ca6b13160a531f"},"schema_version":"1.0"},"canonical_sha256":"960e3e28334b26fef6e4404acb17901bd8be6644485beb26d4563627dd1a5557","source":{"kind":"arxiv","id":"2606.03469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03469","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03469v1","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03469","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"SYHD4KBTJMTP","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_16","alias_value":"SYHD4KBTJMTP55XE","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_8","alias_value":"SYHD4KBT","created_at":"2026-06-03T01:05:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SYHD4KBTJMTP55XEIBFMWF4QDP","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T10:46:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"aef79694717fd3b598e8b65af3cc98ef5c8fbba4aed74b41f61a466156416efa","abstract_canon_sha256":"72f2941dbd70d24a8a2cf555944c76212fe32ae04711795e42ca6b13160a531f"},"schema_version":"1.0"},"canonical_sha256":"960e3e28334b26fef6e4404acb17901bd8be6644485beb26d4563627dd1a5557","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:58.720040Z","signature_b64":"sjbHH/tn8crXTk8bmlB9bcdYWNwguyH4dw3uWN5dJ0df9omGoNRQgEq94yTLIwICbCWLKmSTK7AqREnxE4/UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"960e3e28334b26fef6e4404acb17901bd8be6644485beb26d4563627dd1a5557","last_reissued_at":"2026-06-03T01:05:58.719700Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:58.719700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03469","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":"2026-06-03T01:05:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrTxFu5N8+yByXYxkKhIsjBKou62W73LKyZLy7DHS6iJwEGYNd9PMH6uUP+t2GoWfRi0PAyxgAvEq+RILtHnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:40:13.343871Z"},"content_sha256":"ab88f67f86b0e025d28d11bd9d53ba8d1ae8a99bf96e01303078634baecce4fb","schema_version":"1.0","event_id":"sha256:ab88f67f86b0e025d28d11bd9d53ba8d1ae8a99bf96e01303078634baecce4fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SYHD4KBTJMTP55XEIBFMWF4QDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Physics-guided correction for operator learning under model misspecification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hao Wu, Lei Ma, Ling Guo, Nicolas Boull\\'e, Yu-Sen Yang","submitted_at":"2026-06-02T10:46:40Z","abstract_excerpt":"Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with governing physical laws. However, most existing methods implicitly assume that the prescribed governing equation is accurate. This assumption may fail in practical applications, where model simplifications, missing physical effects, parameter drift, or incomplete constitutive relations can lead to model misspecification. In this work, we propose a physics-guided operator correction framework for learning solution operator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03469","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/2606.03469/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":"2026-06-03T01:05:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eLcF8fzo3GIebHLVIs6CJG21XcNdK83JW2lGvcqrdflriXqFJQlE/QXfYiQR3jLfDjLfIGRFamvEvjX6w2vPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:40:13.344635Z"},"content_sha256":"37b8c219f002aa9b74d3d648e163afe58a177c6d89b5686220038fb89aabde03","schema_version":"1.0","event_id":"sha256:37b8c219f002aa9b74d3d648e163afe58a177c6d89b5686220038fb89aabde03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/bundle.json","state_url":"https://pith.science/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/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":"2026-06-08T10:40:13Z","links":{"resolver":"https://pith.science/pith/SYHD4KBTJMTP55XEIBFMWF4QDP","bundle":"https://pith.science/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/bundle.json","state":"https://pith.science/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYHD4KBTJMTP55XEIBFMWF4QDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SYHD4KBTJMTP55XEIBFMWF4QDP","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":"72f2941dbd70d24a8a2cf555944c76212fe32ae04711795e42ca6b13160a531f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T10:46:40Z","title_canon_sha256":"aef79694717fd3b598e8b65af3cc98ef5c8fbba4aed74b41f61a466156416efa"},"schema_version":"1.0","source":{"id":"2606.03469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03469","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03469v1","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03469","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"SYHD4KBTJMTP","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_16","alias_value":"SYHD4KBTJMTP55XE","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_8","alias_value":"SYHD4KBT","created_at":"2026-06-03T01:05:58Z"}],"graph_snapshots":[{"event_id":"sha256:37b8c219f002aa9b74d3d648e163afe58a177c6d89b5686220038fb89aabde03","target":"graph","created_at":"2026-06-03T01:05:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.03469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with governing physical laws. However, most existing methods implicitly assume that the prescribed governing equation is accurate. This assumption may fail in practical applications, where model simplifications, missing physical effects, parameter drift, or incomplete constitutive relations can lead to model misspecification. In this work, we propose a physics-guided operator correction framework for learning solution operator","authors_text":"Hao Wu, Lei Ma, Ling Guo, Nicolas Boull\\'e, Yu-Sen Yang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T10:46:40Z","title":"Physics-guided correction for operator learning under model misspecification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03469","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:ab88f67f86b0e025d28d11bd9d53ba8d1ae8a99bf96e01303078634baecce4fb","target":"record","created_at":"2026-06-03T01:05:58Z","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":"72f2941dbd70d24a8a2cf555944c76212fe32ae04711795e42ca6b13160a531f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T10:46:40Z","title_canon_sha256":"aef79694717fd3b598e8b65af3cc98ef5c8fbba4aed74b41f61a466156416efa"},"schema_version":"1.0","source":{"id":"2606.03469","kind":"arxiv","version":1}},"canonical_sha256":"960e3e28334b26fef6e4404acb17901bd8be6644485beb26d4563627dd1a5557","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"960e3e28334b26fef6e4404acb17901bd8be6644485beb26d4563627dd1a5557","first_computed_at":"2026-06-03T01:05:58.719700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:58.719700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sjbHH/tn8crXTk8bmlB9bcdYWNwguyH4dw3uWN5dJ0df9omGoNRQgEq94yTLIwICbCWLKmSTK7AqREnxE4/UCg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:58.720040Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab88f67f86b0e025d28d11bd9d53ba8d1ae8a99bf96e01303078634baecce4fb","sha256:37b8c219f002aa9b74d3d648e163afe58a177c6d89b5686220038fb89aabde03"],"state_sha256":"56573c363652c122a0c822c15b25418ac66d86e8ebf2b0c4dd849fab539cfed8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIoDSmkgeRV+ZBNpLDNE8qu/q3/4k033SVkr1da/YRcvI2CB5gMr9ClawT40AnVPVDbEs5YHJqIZRsBjfpJUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:40:13.349116Z","bundle_sha256":"923982ec7eb0a8aa449073e4322069ab33ed33dae1676452ef118b6a40ad07ff"}}