{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:XGMCWXRZ6LQC4HJ5R5G7AXSYIH","short_pith_number":"pith:XGMCWXRZ","canonical_record":{"source":{"id":"2211.05560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-11-10T13:29:15Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"7841310404b8e6cc9d40202eb32f64b62529cebc21326b7254fbfd2025bb0e0e","abstract_canon_sha256":"f74f85d41d1151eef65ceefce059cafaa56c50700576dc5be80549fdba2be777"},"schema_version":"1.0"},"canonical_sha256":"b9982b5e39f2e02e1d3d8f4df05e5841e677155a92b0fda74723eea2aa33dc61","source":{"kind":"arxiv","id":"2211.05560","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.05560","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2211.05560v2","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.05560","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"XGMCWXRZ6LQC","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"XGMCWXRZ6LQC4HJ5","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"XGMCWXRZ","created_at":"2026-07-05T06:11:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:XGMCWXRZ6LQC4HJ5R5G7AXSYIH","target":"record","payload":{"canonical_record":{"source":{"id":"2211.05560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-11-10T13:29:15Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"7841310404b8e6cc9d40202eb32f64b62529cebc21326b7254fbfd2025bb0e0e","abstract_canon_sha256":"f74f85d41d1151eef65ceefce059cafaa56c50700576dc5be80549fdba2be777"},"schema_version":"1.0"},"canonical_sha256":"b9982b5e39f2e02e1d3d8f4df05e5841e677155a92b0fda74723eea2aa33dc61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:57.896882Z","signature_b64":"N74ITG/KUCZQTkzoSCJBhjrThX3+ita1g+Qp0Dvmyarfm4DO1xOEK0NR9+KGcK6XjafI7S6huhVz96n9ysAbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9982b5e39f2e02e1d3d8f4df05e5841e677155a92b0fda74723eea2aa33dc61","last_reissued_at":"2026-07-05T06:11:57.896449Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:57.896449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.05560","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":"2026-07-05T06:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0IAWBR98oSOwZ1f7FxsueHkNKEcd0dSObs/5ra37Yv7Yw+x/Q2igzm4hzUIgIriXUU1UvU77pfyPAoQdR6YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:32:16.145463Z"},"content_sha256":"a294093ef73b896c2df6cd533f951cbda339327ae286fdc4839c7a2ce7f97bc5","schema_version":"1.0","event_id":"sha256:a294093ef73b896c2df6cd533f951cbda339327ae286fdc4839c7a2ce7f97bc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:XGMCWXRZ6LQC4HJ5R5G7AXSYIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite basis physics-informed neural networks as a Schwarz domain decomposition method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Alexander Heinlein, Ben Moseley, Siddhartha Mishra, Victorita Dolean","submitted_at":"2022-11-10T13:29:15Z","abstract_excerpt":"Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to incorporate the residual of the PDE as well as boundary conditions into its loss function when training it. This provides a simple and mesh-free approach for solving problems relating to PDEs. However, a key limitation of PINNs is their lack of accuracy and efficiency when solving problems with larger domains and more complex, multi-scale solutions. In a more re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.05560","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/2211.05560/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":"2026-07-05T06:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEi7VAlQ9ZSFoR4DkUzdYyFaCk0kiH3Q8LOZlR7qn2zEpNlYVMgdER711CFWWhhwpK0G380ImbczVBexoxV3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:32:16.145849Z"},"content_sha256":"1adf72f9896bf0024e6a6287adec9532d675957593b19b2207f4b99efa3d7f6c","schema_version":"1.0","event_id":"sha256:1adf72f9896bf0024e6a6287adec9532d675957593b19b2207f4b99efa3d7f6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/bundle.json","state_url":"https://pith.science/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/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":"2026-08-03T16:32:16Z","links":{"resolver":"https://pith.science/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH","bundle":"https://pith.science/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/bundle.json","state":"https://pith.science/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGMCWXRZ6LQC4HJ5R5G7AXSYIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XGMCWXRZ6LQC4HJ5R5G7AXSYIH","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":"f74f85d41d1151eef65ceefce059cafaa56c50700576dc5be80549fdba2be777","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-11-10T13:29:15Z","title_canon_sha256":"7841310404b8e6cc9d40202eb32f64b62529cebc21326b7254fbfd2025bb0e0e"},"schema_version":"1.0","source":{"id":"2211.05560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.05560","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2211.05560v2","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.05560","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"XGMCWXRZ6LQC","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"XGMCWXRZ6LQC4HJ5","created_at":"2026-07-05T06:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"XGMCWXRZ","created_at":"2026-07-05T06:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:1adf72f9896bf0024e6a6287adec9532d675957593b19b2207f4b99efa3d7f6c","target":"graph","created_at":"2026-07-05T06:11:57Z","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/2211.05560/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to incorporate the residual of the PDE as well as boundary conditions into its loss function when training it. This provides a simple and mesh-free approach for solving problems relating to PDEs. However, a key limitation of PINNs is their lack of accuracy and efficiency when solving problems with larger domains and more complex, multi-scale solutions. In a more re","authors_text":"Alexander Heinlein, Ben Moseley, Siddhartha Mishra, Victorita Dolean","cross_cats":["cs.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-11-10T13:29:15Z","title":"Finite basis physics-informed neural networks as a Schwarz domain decomposition method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.05560","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:a294093ef73b896c2df6cd533f951cbda339327ae286fdc4839c7a2ce7f97bc5","target":"record","created_at":"2026-07-05T06:11:57Z","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":"f74f85d41d1151eef65ceefce059cafaa56c50700576dc5be80549fdba2be777","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-11-10T13:29:15Z","title_canon_sha256":"7841310404b8e6cc9d40202eb32f64b62529cebc21326b7254fbfd2025bb0e0e"},"schema_version":"1.0","source":{"id":"2211.05560","kind":"arxiv","version":2}},"canonical_sha256":"b9982b5e39f2e02e1d3d8f4df05e5841e677155a92b0fda74723eea2aa33dc61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9982b5e39f2e02e1d3d8f4df05e5841e677155a92b0fda74723eea2aa33dc61","first_computed_at":"2026-07-05T06:11:57.896449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:57.896449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N74ITG/KUCZQTkzoSCJBhjrThX3+ita1g+Qp0Dvmyarfm4DO1xOEK0NR9+KGcK6XjafI7S6huhVz96n9ysAbAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:57.896882Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.05560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a294093ef73b896c2df6cd533f951cbda339327ae286fdc4839c7a2ce7f97bc5","sha256:1adf72f9896bf0024e6a6287adec9532d675957593b19b2207f4b99efa3d7f6c"],"state_sha256":"6407eb872c12efc69e5fade458fdc1edfe1704cf41e21ceb88bb0d2dc885183f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tTu8o7z5WUNQxBcW4Zy2NMvN3jyu/pVSy/A4CalRyPRX7Gjvhc3qU8sv4WCHL237QHR0jdRdolJiq6wemX2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:32:16.149029Z","bundle_sha256":"3cc950ed2977cdfdfadf5467d2e248506a9d50e8227bf04f3b9347c73781b2ce"}}