{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:I5RI5Z5S4WWFC6WONLUSNVUSET","short_pith_number":"pith:I5RI5Z5S","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"},"canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","source":{"kind":"arxiv","id":"2606.02335","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02335","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02335v1","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02335","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"I5RI5Z5S4WWF","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"I5RI5Z5S4WWFC6WO","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"I5RI5Z5S","created_at":"2026-06-02T03:04:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:I5RI5Z5S4WWFC6WONLUSNVUSET","target":"record","payload":{"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"},"canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","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"},"source_kind":"arxiv","source_id":"2606.02335","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":"2026-06-02T03:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBVJs8Kx06VEbWSVzZ/xJeS3dszcGNPsaSaymHHKskFYc0WWLXZ8a5Q5BgLYgVZ44oxewEDsBw/1kpAM0U84Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:36:45.658132Z"},"content_sha256":"1bcdd7faad0404729f7690eff3c838a08ea3752e1bcb536f2e5cb154bd8078be","schema_version":"1.0","event_id":"sha256:1bcdd7faad0404729f7690eff3c838a08ea3752e1bcb536f2e5cb154bd8078be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:I5RI5Z5S4WWFC6WONLUSNVUSET","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+AdkXzWdmS1stV+TBPPe1tTDUGfIVn96ErIIl0yPOimmpDd49RCjBw7eKj6vb/+FaT+rxYqWPU12p1hDQAjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:36:45.658522Z"},"content_sha256":"30d3d321f54e64af2e37100d368cd4420e42ef4eaebbb382f7bad0ef2c4d51e9","schema_version":"1.0","event_id":"sha256:30d3d321f54e64af2e37100d368cd4420e42ef4eaebbb382f7bad0ef2c4d51e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/bundle.json","state_url":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/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":"2026-06-30T03:36:45Z","links":{"resolver":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET","bundle":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/bundle.json","state":"https://pith.science/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5RI5Z5S4WWFC6WONLUSNVUSET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I5RI5Z5S4WWFC6WONLUSNVUSET","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":"d33fc7afb2679c1fb0d1e6e395fd0d525c2da257b45ec6b55d334f4e77070985","cross_cats_sorted":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-06-01T14:44:48Z","title_canon_sha256":"13b59dad2be152e4056c7184415359aa9c02f7246efab8365a68c4e1c0da3214"},"schema_version":"1.0","source":{"id":"2606.02335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02335","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02335v1","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02335","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"I5RI5Z5S4WWF","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"I5RI5Z5S4WWFC6WO","created_at":"2026-06-02T03:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"I5RI5Z5S","created_at":"2026-06-02T03:04:56Z"}],"graph_snapshots":[{"event_id":"sha256:30d3d321f54e64af2e37100d368cd4420e42ef4eaebbb382f7bad0ef2c4d51e9","target":"graph","created_at":"2026-06-02T03:04:56Z","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/2606.02335/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Conrard Giresse Tetsassi Feugmo, David Pankaczy","cross_cats":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-06-01T14:44:48Z","title":"Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02335","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":"sha256:1bcdd7faad0404729f7690eff3c838a08ea3752e1bcb536f2e5cb154bd8078be","target":"record","created_at":"2026-06-02T03:04:56Z","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":"d33fc7afb2679c1fb0d1e6e395fd0d525c2da257b45ec6b55d334f4e77070985","cross_cats_sorted":["math-ph","math.MP","physics.app-ph","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-06-01T14:44:48Z","title_canon_sha256":"13b59dad2be152e4056c7184415359aa9c02f7246efab8365a68c4e1c0da3214"},"schema_version":"1.0","source":{"id":"2606.02335","kind":"arxiv","version":1}},"canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47628ee7b2e5ac517ace6ae926d69224e3484e038978fa04bf8cd7ff211782da","first_computed_at":"2026-06-02T03:04:56.396287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:56.396287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lg9u/VwFiA3AtJ4xvPgyVK0cgMew8KqiPbrNG/ONqAv/fB8yJYO7SnjabqdAF72fJkyEVQP2w9gAVfMyCUknDA==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:56.396638Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bcdd7faad0404729f7690eff3c838a08ea3752e1bcb536f2e5cb154bd8078be","sha256:30d3d321f54e64af2e37100d368cd4420e42ef4eaebbb382f7bad0ef2c4d51e9"],"state_sha256":"bf06eda810fc7ade1a7ebca7c70c1102a62af69801961cf6280a3f771e5488d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrXZRxjKnL7TETOEUbwlIEbJjLLV6EO11Zxkr4P9bMpKscYrpH9mhWczpK6sccQgnEG06pQiy6Gbx6pfV/u0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:36:45.660477Z","bundle_sha256":"7bfc021dd9f69c6bf24f2120e1d761968e35d98319bc8b824b4cf002d62c16f3"}}