{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PKZGVEKSVT4UDGC6SHJZ3VMZYG","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":"a2e55ef51ef76c69ba7598ea357065b2a6651fb982fe7b48481595703ff7d829","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T05:31:45Z","title_canon_sha256":"fc7aa0248b2f7bcd15d7bf6471e7c9c6ed769f3773f1b03b6a177a9f0c32f069"},"schema_version":"1.0","source":{"id":"2407.03347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03347","created_at":"2026-07-05T08:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03347v1","created_at":"2026-07-05T08:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03347","created_at":"2026-07-05T08:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"PKZGVEKSVT4U","created_at":"2026-07-05T08:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"PKZGVEKSVT4UDGC6","created_at":"2026-07-05T08:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"PKZGVEKS","created_at":"2026-07-05T08:39:53Z"}],"graph_snapshots":[{"event_id":"sha256:1f9caeea06e057040a1d8051cc338b62c3c9087d261feccdb091c9dbf342ade3","target":"graph","created_at":"2026-07-05T08:39:53Z","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/2407.03347/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this study is to utilize the Chebyshev spectral method neural network(CSNN) model to solve differential equations. This approach employs a single-layer neural network wherein Chebyshev spectral methods are used to construct neurons satisfying boundary conditions. The study uses a feedforward neural network model and error backpropagation principles, utilizing automatic differentiation (AD) to compute the loss function. This method avoids the need to solve non-sparse linear systems, making it convenient for algorithm implementation and solving high-dimensional problems. The uniqu","authors_text":"Pengsong Yin, Shuo Ling, Wenjun Ying","cross_cats":["cs.LG","cs.NA","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T05:31:45Z","title":"Chebyshev Spectral Neural Networks for Solving Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03347","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":"sha256:63762af979268613ce2f29ce009b4f4086e17e897ab8af5c76cf2a2dabb1fa67","target":"record","created_at":"2026-07-05T08:39:53Z","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":"a2e55ef51ef76c69ba7598ea357065b2a6651fb982fe7b48481595703ff7d829","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T05:31:45Z","title_canon_sha256":"fc7aa0248b2f7bcd15d7bf6471e7c9c6ed769f3773f1b03b6a177a9f0c32f069"},"schema_version":"1.0","source":{"id":"2407.03347","kind":"arxiv","version":1}},"canonical_sha256":"7ab26a9152acf941985e91d39dd599c1bdd0b7b656856d8171c02a327f01ebb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ab26a9152acf941985e91d39dd599c1bdd0b7b656856d8171c02a327f01ebb7","first_computed_at":"2026-07-05T08:39:53.522544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:53.522544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUJpFnTm3Mz9FVSwSTJh6gVyD3wTVMRUNDfxaNxyTi5jzHHbDXSndaHQ/TbYaSzsU0MjJ+xx9C3TFvErkiirDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:53.522922Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.03347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63762af979268613ce2f29ce009b4f4086e17e897ab8af5c76cf2a2dabb1fa67","sha256:1f9caeea06e057040a1d8051cc338b62c3c9087d261feccdb091c9dbf342ade3"],"state_sha256":"c50313597cb8cbb80e27872fe0e3d7932b17ed1a302f8dca895e3e8cac56993c"}