{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5BERCS5P5ZJDC4TQVSRBAW45DR","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":"ec6b35cfbdf10c1faeb1985dc5c2d288a660523980198abc001749dd4a3e7348","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-28T22:11:00Z","title_canon_sha256":"486595b7863d06a625b6e84c822954e9081a806f77b4a22377ef8bce739591fd"},"schema_version":"1.0","source":{"id":"2506.23024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23024","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23024v1","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23024","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"5BERCS5P5ZJD","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"5BERCS5P5ZJDC4TQ","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"5BERCS5P","created_at":"2026-07-05T11:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:551686cdd246a5b385a9bf82d03058bbcfe7bb9ef5961b905d04dd964a0ba2f4","target":"graph","created_at":"2026-07-05T11:28:49Z","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/2506.23024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural networks (PINNs) offer a flexible way to solve partial differential equations (PDEs) with machine learning, yet they still fall well short of the machine-precision accuracy many scientific tasks demand. In this work, we investigate whether the precision ceiling comes from the ill-conditioning of the PDEs or from the typical multi-layer perceptron (MLP) architecture. We introduce the Barycentric Weight Layer (BWLer), which models the PDE solution through barycentric polynomial interpolation. A BWLer can be added on top of an existing MLP (a BWLer-hat) or replace it compl","authors_text":"Atri Rudra, Chris R\\'e, Denise Hui Jean Lee, Jerry Liu, Rajat Vadiraj Dwaraknath, Yasa Baig","cross_cats":["cs.AI","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-28T22:11:00Z","title":"BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23024","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:db083150d1f6854a50175dbddab11892d31a5948ffe7e4911151481f11fb0954","target":"record","created_at":"2026-07-05T11:28:49Z","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":"ec6b35cfbdf10c1faeb1985dc5c2d288a660523980198abc001749dd4a3e7348","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-28T22:11:00Z","title_canon_sha256":"486595b7863d06a625b6e84c822954e9081a806f77b4a22377ef8bce739591fd"},"schema_version":"1.0","source":{"id":"2506.23024","kind":"arxiv","version":1}},"canonical_sha256":"e849114bafee52317270aca2105b9d1c4bd57ae2b472c61ed0b26ab0f205cb92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e849114bafee52317270aca2105b9d1c4bd57ae2b472c61ed0b26ab0f205cb92","first_computed_at":"2026-07-05T11:28:49.348975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:49.348975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqJQVtnOGZNsUQBXg9o0Ktw3T+VLEB660WqvzGae2xGpxDsHlcB81TV7eVawYjQHlsTWNK99pmkmFlUFZfEQDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:49.349487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.23024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db083150d1f6854a50175dbddab11892d31a5948ffe7e4911151481f11fb0954","sha256:551686cdd246a5b385a9bf82d03058bbcfe7bb9ef5961b905d04dd964a0ba2f4"],"state_sha256":"f91f70c384118c18a4f518226efb189b8954fdcb15dd1389cb19acc5cded8519"}