{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ETVCMJB4W2WJFYRHP432V6TZ2Z","short_pith_number":"pith:ETVCMJB4","canonical_record":{"source":{"id":"2212.07477","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-14T19:54:46Z","cross_cats_sorted":["math.AP","math.OA"],"title_canon_sha256":"5cc7ad35a76c7eea7c6e2592f73b4cc1e7dec4bd12d3d29cf492b5514f40fd97","abstract_canon_sha256":"943f3bfcfd2880f9385e8f06a22e0ae3f72157c00fc6d3363b8a1617aa1ca119"},"schema_version":"1.0"},"canonical_sha256":"24ea26243cb6ac92e2277f37aafa79d67d7b62dcc7c5ac117ec4ad848e185be4","source":{"kind":"arxiv","id":"2212.07477","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.07477","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"arxiv_version","alias_value":"2212.07477v2","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.07477","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_12","alias_value":"ETVCMJB4W2WJ","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_16","alias_value":"ETVCMJB4W2WJFYRH","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_8","alias_value":"ETVCMJB4","created_at":"2026-07-05T05:47:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ETVCMJB4W2WJFYRHP432V6TZ2Z","target":"record","payload":{"canonical_record":{"source":{"id":"2212.07477","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-14T19:54:46Z","cross_cats_sorted":["math.AP","math.OA"],"title_canon_sha256":"5cc7ad35a76c7eea7c6e2592f73b4cc1e7dec4bd12d3d29cf492b5514f40fd97","abstract_canon_sha256":"943f3bfcfd2880f9385e8f06a22e0ae3f72157c00fc6d3363b8a1617aa1ca119"},"schema_version":"1.0"},"canonical_sha256":"24ea26243cb6ac92e2277f37aafa79d67d7b62dcc7c5ac117ec4ad848e185be4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:34.058915Z","signature_b64":"UaJNOuhtnQP3izTwFQAjzpGYaCUYscuxL3bm/Yxeb3kdASV6rbX9yYLVqvEG46K1NlLTCBpQ2CQqxqU7yfI1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24ea26243cb6ac92e2277f37aafa79d67d7b62dcc7c5ac117ec4ad848e185be4","last_reissued_at":"2026-07-05T05:47:34.058370Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:34.058370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.07477","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:47:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WF/Z+grqhIfr8pNLR3QcIMJWZHQEoN9Bq1t87aV/zs6ao61KrHOSHd7dKSjG0FKrFVFtwp6u9x/L3sl3896iDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:43:57.307659Z"},"content_sha256":"23ce1f5ac7605625acb01e7a418417775e693463b3e4494d41cdeda4414d34c1","schema_version":"1.0","event_id":"sha256:23ce1f5ac7605625acb01e7a418417775e693463b3e4494d41cdeda4414d34c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ETVCMJB4W2WJFYRHP432V6TZ2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Guiding continuous operator learning through Physics-based boundary constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.OA"],"primary_cat":"cs.LG","authors_text":"Danielle C. Maddix, Gaurav Gupta, Nadim Saad, Shima Alizadeh","submitted_at":"2022-12-14T19:54:46Z","abstract_excerpt":"Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical meaning, and guarantee the existence and the uniqueness of the PDE solution. Current neural-network based approaches that aim to solve PDEs rely only on training data to help the model learn BCs implicitly. There is no guarantee of BC satisfaction by these models during evaluation. In this work, we propose Boundary enforcing Operator Network (BOON) that enable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07477","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/2212.07477/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":"2026-07-05T05:47:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dj8HAJ/PntlWMyBf2gUx7A2aiNGIRu0/NOg5pfhkTxki54INP1lG8jLZl8wPngDZnuoyhC0y4n8N8TlgyMzeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:43:57.308589Z"},"content_sha256":"40ec3da891a39adb20948864b01588a151dd628017e3e3a2e0d88f1dd9105e63","schema_version":"1.0","event_id":"sha256:40ec3da891a39adb20948864b01588a151dd628017e3e3a2e0d88f1dd9105e63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/bundle.json","state_url":"https://pith.science/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/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":"2026-08-08T00:43:57Z","links":{"resolver":"https://pith.science/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z","bundle":"https://pith.science/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/bundle.json","state":"https://pith.science/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ETVCMJB4W2WJFYRHP432V6TZ2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ETVCMJB4W2WJFYRHP432V6TZ2Z","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":"943f3bfcfd2880f9385e8f06a22e0ae3f72157c00fc6d3363b8a1617aa1ca119","cross_cats_sorted":["math.AP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-14T19:54:46Z","title_canon_sha256":"5cc7ad35a76c7eea7c6e2592f73b4cc1e7dec4bd12d3d29cf492b5514f40fd97"},"schema_version":"1.0","source":{"id":"2212.07477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.07477","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"arxiv_version","alias_value":"2212.07477v2","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.07477","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_12","alias_value":"ETVCMJB4W2WJ","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_16","alias_value":"ETVCMJB4W2WJFYRH","created_at":"2026-07-05T05:47:34Z"},{"alias_kind":"pith_short_8","alias_value":"ETVCMJB4","created_at":"2026-07-05T05:47:34Z"}],"graph_snapshots":[{"event_id":"sha256:40ec3da891a39adb20948864b01588a151dd628017e3e3a2e0d88f1dd9105e63","target":"graph","created_at":"2026-07-05T05:47:34Z","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/2212.07477/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical meaning, and guarantee the existence and the uniqueness of the PDE solution. Current neural-network based approaches that aim to solve PDEs rely only on training data to help the model learn BCs implicitly. There is no guarantee of BC satisfaction by these models during evaluation. In this work, we propose Boundary enforcing Operator Network (BOON) that enable","authors_text":"Danielle C. Maddix, Gaurav Gupta, Nadim Saad, Shima Alizadeh","cross_cats":["math.AP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-14T19:54:46Z","title":"Guiding continuous operator learning through Physics-based boundary constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07477","kind":"arxiv","version":2},"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":"sha256:23ce1f5ac7605625acb01e7a418417775e693463b3e4494d41cdeda4414d34c1","target":"record","created_at":"2026-07-05T05:47:34Z","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":"943f3bfcfd2880f9385e8f06a22e0ae3f72157c00fc6d3363b8a1617aa1ca119","cross_cats_sorted":["math.AP","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-14T19:54:46Z","title_canon_sha256":"5cc7ad35a76c7eea7c6e2592f73b4cc1e7dec4bd12d3d29cf492b5514f40fd97"},"schema_version":"1.0","source":{"id":"2212.07477","kind":"arxiv","version":2}},"canonical_sha256":"24ea26243cb6ac92e2277f37aafa79d67d7b62dcc7c5ac117ec4ad848e185be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24ea26243cb6ac92e2277f37aafa79d67d7b62dcc7c5ac117ec4ad848e185be4","first_computed_at":"2026-07-05T05:47:34.058370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:34.058370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UaJNOuhtnQP3izTwFQAjzpGYaCUYscuxL3bm/Yxeb3kdASV6rbX9yYLVqvEG46K1NlLTCBpQ2CQqxqU7yfI1Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:34.058915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.07477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ce1f5ac7605625acb01e7a418417775e693463b3e4494d41cdeda4414d34c1","sha256:40ec3da891a39adb20948864b01588a151dd628017e3e3a2e0d88f1dd9105e63"],"state_sha256":"3aadf6800d11e6c1dd417c4564f9e7b8d58817e0a215c285eacb9b6850af0bca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMRJMXAa5Ks4YJQ29M73tiR/w2pxdKtbHdXw4HgbuUEKI+w1PEubmKUreu4CmWh6V3J48uxyfuIswx4Cvq/yCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T00:43:57.416427Z","bundle_sha256":"8a241043c891c96af247d5ae952198de0d82d7a30bcbcb6e76185eafd84aadca"}}