{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VR4LEJZUDYKIF7QHTLEPJ6K6IX","short_pith_number":"pith:VR4LEJZU","canonical_record":{"source":{"id":"2110.00352","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-01T12:29:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"559d6b4688f985dedafbfbef7352ecb4d91150f561121b9052c71bd41e81842a","abstract_canon_sha256":"97bd211606d871c34b0e44ceedd3c959754e7a7b1739ceed535200405febe3ff"},"schema_version":"1.0"},"canonical_sha256":"ac78b227341e1482fe079ac8f4f95e45cb1b036a40fc621261c8bbeb06ed5081","source":{"kind":"arxiv","id":"2110.00352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.00352","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"2110.00352v1","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.00352","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"VR4LEJZUDYKI","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_16","alias_value":"VR4LEJZUDYKIF7QH","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_8","alias_value":"VR4LEJZU","created_at":"2026-07-05T03:19:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VR4LEJZUDYKIF7QHTLEPJ6K6IX","target":"record","payload":{"canonical_record":{"source":{"id":"2110.00352","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-01T12:29:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"559d6b4688f985dedafbfbef7352ecb4d91150f561121b9052c71bd41e81842a","abstract_canon_sha256":"97bd211606d871c34b0e44ceedd3c959754e7a7b1739ceed535200405febe3ff"},"schema_version":"1.0"},"canonical_sha256":"ac78b227341e1482fe079ac8f4f95e45cb1b036a40fc621261c8bbeb06ed5081","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:19:28.742269Z","signature_b64":"w/redx3fCVcLfS0iuQJdgtEscGv9Sk2RergsLGKMqML+RZ53T5zCGKqBhqEtbKogMDxbqlMW8PnlpQb7n1iFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac78b227341e1482fe079ac8f4f95e45cb1b036a40fc621261c8bbeb06ed5081","last_reissued_at":"2026-07-05T03:19:28.741797Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:19:28.741797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.00352","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":"2026-07-05T03:19:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exvAPnIdUxNFg1jW/HVocRl1/9hgyysWn7OaEQnuAipvhPbBwLskuzUDM5Bm0hrvKp39aLjgZTTYsVEF1jXmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:24:33.790690Z"},"content_sha256":"596b54a01aeb74ef7086edd1ebcb25e32b87d11be45ffba583972767bcee8f9c","schema_version":"1.0","event_id":"sha256:596b54a01aeb74ef7086edd1ebcb25e32b87d11be45ffba583972767bcee8f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VR4LEJZUDYKIF7QHTLEPJ6K6IX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Fukai Chen, Guochang Lin, Junqing Chen, Jun Wang, Pipi Hu, Xiang Chen, Zuoqiang Shi","submitted_at":"2021-10-01T12:29:41Z","abstract_excerpt":"We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs, BINet learns to solve, as a proxy, associated boundary integral equations using neural networks. The benefits are three-fold. Firstly, only the boundary conditions need to be fitted since the PDE can be automatically satisfied with single or double layer representations according to the potential theory. Secondly, the dimension of the boundary integral equat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.00352","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/2110.00352/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":"2026-07-05T03:19:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAac5UAXhMBNjMGONfqeXYBMxg+yhUbnMWupRtlt5yCrBf4/PM/PBBr/REDAmH8R9CB8eAmuk4qXj5zMOp4XCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:24:33.791067Z"},"content_sha256":"31a34546bff889ac4ca1e62afb8bc6f5cdc259b2ce97ce89a6b78a079201e805","schema_version":"1.0","event_id":"sha256:31a34546bff889ac4ca1e62afb8bc6f5cdc259b2ce97ce89a6b78a079201e805"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/bundle.json","state_url":"https://pith.science/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/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":"2026-07-07T13:24:33Z","links":{"resolver":"https://pith.science/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX","bundle":"https://pith.science/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/bundle.json","state":"https://pith.science/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VR4LEJZUDYKIF7QHTLEPJ6K6IX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VR4LEJZUDYKIF7QHTLEPJ6K6IX","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":"97bd211606d871c34b0e44ceedd3c959754e7a7b1739ceed535200405febe3ff","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-01T12:29:41Z","title_canon_sha256":"559d6b4688f985dedafbfbef7352ecb4d91150f561121b9052c71bd41e81842a"},"schema_version":"1.0","source":{"id":"2110.00352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.00352","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"2110.00352v1","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.00352","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"VR4LEJZUDYKI","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_16","alias_value":"VR4LEJZUDYKIF7QH","created_at":"2026-07-05T03:19:28Z"},{"alias_kind":"pith_short_8","alias_value":"VR4LEJZU","created_at":"2026-07-05T03:19:28Z"}],"graph_snapshots":[{"event_id":"sha256:31a34546bff889ac4ca1e62afb8bc6f5cdc259b2ce97ce89a6b78a079201e805","target":"graph","created_at":"2026-07-05T03:19:28Z","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/2110.00352/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs, BINet learns to solve, as a proxy, associated boundary integral equations using neural networks. The benefits are three-fold. Firstly, only the boundary conditions need to be fitted since the PDE can be automatically satisfied with single or double layer representations according to the potential theory. Secondly, the dimension of the boundary integral equat","authors_text":"Fukai Chen, Guochang Lin, Junqing Chen, Jun Wang, Pipi Hu, Xiang Chen, Zuoqiang Shi","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-01T12:29:41Z","title":"BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.00352","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":"sha256:596b54a01aeb74ef7086edd1ebcb25e32b87d11be45ffba583972767bcee8f9c","target":"record","created_at":"2026-07-05T03:19:28Z","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":"97bd211606d871c34b0e44ceedd3c959754e7a7b1739ceed535200405febe3ff","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-01T12:29:41Z","title_canon_sha256":"559d6b4688f985dedafbfbef7352ecb4d91150f561121b9052c71bd41e81842a"},"schema_version":"1.0","source":{"id":"2110.00352","kind":"arxiv","version":1}},"canonical_sha256":"ac78b227341e1482fe079ac8f4f95e45cb1b036a40fc621261c8bbeb06ed5081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac78b227341e1482fe079ac8f4f95e45cb1b036a40fc621261c8bbeb06ed5081","first_computed_at":"2026-07-05T03:19:28.741797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:28.741797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w/redx3fCVcLfS0iuQJdgtEscGv9Sk2RergsLGKMqML+RZ53T5zCGKqBhqEtbKogMDxbqlMW8PnlpQb7n1iFBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:28.742269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.00352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:596b54a01aeb74ef7086edd1ebcb25e32b87d11be45ffba583972767bcee8f9c","sha256:31a34546bff889ac4ca1e62afb8bc6f5cdc259b2ce97ce89a6b78a079201e805"],"state_sha256":"bc35b3626b7e82911d59461cc08141a256a86056c3e2b0dead2a7cfdd8d25f37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"axvfq1xcQhtPfCy0SvclxLqPMJ3mjRKJzMecs7GrWKn7Fv20s6LB3KX+IOh8D0q9iUsWziIkgFkTaGVwouESAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:24:33.793097Z","bundle_sha256":"5d7cb2e47259531fddb42ccd9b842c2e6db002d5338b876200245e1db1c728ee"}}