{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:GFYZJBZKIP4OLZQA5D7HWBUEZY","short_pith_number":"pith:GFYZJBZK","canonical_record":{"source":{"id":"2410.18153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"title_canon_sha256":"38f8226edeab32add525d0c2f3dd6d57da9c105aefca14aacd128c32017df29a","abstract_canon_sha256":"554f3a476404fcebd5cc002ca233583a0e663953de0e02f12a1f652c8d32831b"},"schema_version":"1.0"},"canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","source":{"kind":"arxiv","id":"2410.18153","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18153","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18153v1","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18153","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"GFYZJBZKIP4O","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"GFYZJBZKIP4OLZQA","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"GFYZJBZK","created_at":"2026-07-05T09:25:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:GFYZJBZKIP4OLZQA5D7HWBUEZY","target":"record","payload":{"canonical_record":{"source":{"id":"2410.18153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"title_canon_sha256":"38f8226edeab32add525d0c2f3dd6d57da9c105aefca14aacd128c32017df29a","abstract_canon_sha256":"554f3a476404fcebd5cc002ca233583a0e663953de0e02f12a1f652c8d32831b"},"schema_version":"1.0"},"canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:25:04.297402Z","signature_b64":"+ibFg9zo09hwLawyjc4u+N91Ld0jtBFdBisI3vxYFLBbr/lXQ1iNQjDA/UIc29H7ksbdQy7Px7KN5J6JjXgxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","last_reissued_at":"2026-07-05T09:25:04.296999Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:25:04.296999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.18153","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":"2026-07-05T09:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTb06qtpD932wEyBVHM+tnN2tMo6MUmUtpts1GAkZYKSPHmjMg5mc7vhaWb4eoI9tqf69rDa0/4Fz8ife99oDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T05:50:31.669109Z"},"content_sha256":"599573422151643f920533e5d5a1b1af080c59960f41a3568a835dcd14f1b8c6","schema_version":"1.0","event_id":"sha256:599573422151643f920533e5d5a1b1af080c59960f41a3568a835dcd14f1b8c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:GFYZJBZKIP4OLZQA5D7HWBUEZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"primary_cat":"math.NA","authors_text":"Taiki Miyagawa, Takeru Yokota","submitted_at":"2024-10-23T06:16:35Z","abstract_excerpt":"We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \\textit{cylindrical approximation}. The cylindrical approximation e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18153","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/2410.18153/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":"2026-07-05T09:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CsZbFtDsx0OgT/dYzHAVCtlbpgl+PBTmD6NHM2IbBdgrNBFMJ9/y7WgeS+vY5bgLWmyrNwdPSrWOyYFflyVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T05:50:31.669691Z"},"content_sha256":"bbb01b759bf9ed0f9671bb1c0283bfa4d483683f200f5e01113aacc3fcba1292","schema_version":"1.0","event_id":"sha256:bbb01b759bf9ed0f9671bb1c0283bfa4d483683f200f5e01113aacc3fcba1292"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/bundle.json","state_url":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/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":"2026-08-03T05:50:31Z","links":{"resolver":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY","bundle":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/bundle.json","state":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GFYZJBZKIP4OLZQA5D7HWBUEZY","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":"554f3a476404fcebd5cc002ca233583a0e663953de0e02f12a1f652c8d32831b","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","title_canon_sha256":"38f8226edeab32add525d0c2f3dd6d57da9c105aefca14aacd128c32017df29a"},"schema_version":"1.0","source":{"id":"2410.18153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18153","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18153v1","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18153","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"GFYZJBZKIP4O","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"GFYZJBZKIP4OLZQA","created_at":"2026-07-05T09:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"GFYZJBZK","created_at":"2026-07-05T09:25:04Z"}],"graph_snapshots":[{"event_id":"sha256:bbb01b759bf9ed0f9671bb1c0283bfa4d483683f200f5e01113aacc3fcba1292","target":"graph","created_at":"2026-07-05T09:25:04Z","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/2410.18153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \\textit{cylindrical approximation}. The cylindrical approximation e","authors_text":"Taiki Miyagawa, Takeru Yokota","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","title":"Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18153","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":"sha256:599573422151643f920533e5d5a1b1af080c59960f41a3568a835dcd14f1b8c6","target":"record","created_at":"2026-07-05T09:25:04Z","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":"554f3a476404fcebd5cc002ca233583a0e663953de0e02f12a1f652c8d32831b","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","title_canon_sha256":"38f8226edeab32add525d0c2f3dd6d57da9c105aefca14aacd128c32017df29a"},"schema_version":"1.0","source":{"id":"2410.18153","kind":"arxiv","version":1}},"canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","first_computed_at":"2026-07-05T09:25:04.296999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:04.296999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ibFg9zo09hwLawyjc4u+N91Ld0jtBFdBisI3vxYFLBbr/lXQ1iNQjDA/UIc29H7ksbdQy7Px7KN5J6JjXgxAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:04.297402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:599573422151643f920533e5d5a1b1af080c59960f41a3568a835dcd14f1b8c6","sha256:bbb01b759bf9ed0f9671bb1c0283bfa4d483683f200f5e01113aacc3fcba1292"],"state_sha256":"85961feea9c51a2a58cc5b9c9be3709fde5b5064418ca7290dd0107a48ffc5dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iHA+WPm6wDT/Vn17DMHA6mYBRlu5I8hFEXgt+BlaffrTqfH2R3t07t7/OygOUH/vpYkeymOVHyBNs7+p4ffrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T05:50:31.674661Z","bundle_sha256":"6af7f4ac8a94925eecf01a643c0f24160f12c5d2703a781fdabab82ee574031b"}}