{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:I5RI5Z5S4WWFC6WONLUSNVUSET","short_pith_number":"pith:I5RI5Z5S","schema_version":"1.0","canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","source":{"kind":"arxiv","id":"2606.02335","version":1},"attestation_state":"computed","paper":{"title":"Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Conrard Giresse Tetsassi Feugmo, David Pankaczy","submitted_at":"2026-06-01T14:44:48Z","abstract_excerpt":"The Neural Spectral Element Method (NSEM) evaluates each network only at fixed Legendre-Gauss-Lobatto quadrature nodes and replaces all derivative calls with precomputed spectral differentiation matrices. The resulting deterministic loss enables limited-memory BFGS (L-BFGS) to reach residuals of 10^-9 to 10^-10. A Kosloff-Tal-Ezer coordinate map resolves electrochemical boundary layers, while a mesh-free neural mortar framework couples multi-element domains. On the four-example Poisson-Nernst-Planck (PNP) benchmark of Huang and co-workers, NSEM attains 10^-4 to 10^-7 relative pointwise error w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.02335","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-06-01T14:44:48Z","cross_cats_sorted":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"title_canon_sha256":"13b59dad2be152e4056c7184415359aa9c02f7246efab8365a68c4e1c0da3214","abstract_canon_sha256":"d33fc7afb2679c1fb0d1e6e395fd0d525c2da257b45ec6b55d334f4e77070985"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:56.396638Z","signature_b64":"lg9u/VwFiA3AtJ4xvPgyVK0cgMew8KqiPbrNG/ONqAv/fB8yJYO7SnjabqdAF72fJkyEVQP2w9gAVfMyCUknDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","last_reissued_at":"2026-06-02T03:04:56.396287Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:56.396287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Conrard Giresse Tetsassi Feugmo, David Pankaczy","submitted_at":"2026-06-01T14:44:48Z","abstract_excerpt":"The Neural Spectral Element Method (NSEM) evaluates each network only at fixed Legendre-Gauss-Lobatto quadrature nodes and replaces all derivative calls with precomputed spectral differentiation matrices. The resulting deterministic loss enables limited-memory BFGS (L-BFGS) to reach residuals of 10^-9 to 10^-10. A Kosloff-Tal-Ezer coordinate map resolves electrochemical boundary layers, while a mesh-free neural mortar framework couples multi-element domains. On the four-example Poisson-Nernst-Planck (PNP) benchmark of Huang and co-workers, NSEM attains 10^-4 to 10^-7 relative pointwise error w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02335","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/2606.02335/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.02335","created_at":"2026-06-02T03:04:56.396357+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.02335v1","created_at":"2026-06-02T03:04:56.396357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02335","created_at":"2026-06-02T03:04:56.396357+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5RI5Z5S4WWF","created_at":"2026-06-02T03:04:56.396357+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5RI5Z5S4WWFC6WO","created_at":"2026-06-02T03:04:56.396357+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5RI5Z5S","created_at":"2026-06-02T03:04:56.396357+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET","json":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET.json","graph_json":"https://pith.science/api/pith-number/I5RI5Z5S4WWFC6WONLUSNVUSET/graph.json","events_json":"https://pith.science/api/pith-number/I5RI5Z5S4WWFC6WONLUSNVUSET/events.json","paper":"https://pith.science/paper/I5RI5Z5S"},"agent_actions":{"view_html":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET","download_json":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET.json","view_paper":"https://pith.science/paper/I5RI5Z5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.02335&json=true","fetch_graph":"https://pith.science/api/pith-number/I5RI5Z5S4WWFC6WONLUSNVUSET/graph.json","fetch_events":"https://pith.science/api/pith-number/I5RI5Z5S4WWFC6WONLUSNVUSET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/action/storage_attestation","attest_author":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/action/author_attestation","sign_citation":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/action/citation_signature","submit_replication":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/action/replication_record"}},"created_at":"2026-06-02T03:04:56.396357+00:00","updated_at":"2026-06-02T03:04:56.396357+00:00"}