{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FEEUZHCXXQQPD3UFTCHP66EV3T","short_pith_number":"pith:FEEUZHCX","schema_version":"1.0","canonical_sha256":"29094c9c57bc20f1ee85988eff7895dccdf0da4cbf342923a0f57e3bd345e737","source":{"kind":"arxiv","id":"2512.09165","version":2},"attestation_state":"computed","paper":{"title":"Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Muhammad Abid, Omer San","submitted_at":"2025-12-09T22:26:29Z","abstract_excerpt":"Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk network, which operates directly on raw spatial or spatiotemporal coordinates through fully connected layers, often struggles to represent sharp gradients, boundary layers, and other non-periodic solution structures on bounded domains. To address these limitations, we introduce the Spectral-Embedded Deep Operator Network (SEDONet), a novel DeepONet architectur"},"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":"2512.09165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-09T22:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"b1fc5469bae93f100e2e860ffbe88c057e6c3f4b3a1f94f8bb8069690f7d6b91","abstract_canon_sha256":"d8f660cf938741cdd3be5bd818f32c350096cc0ae39c834de4168334c5e76be3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:30.610637Z","signature_b64":"dZR6DPXUnfw69Dj4bdpnH1dUheso5bBddd5LNo2avcxtJJS58D+AebPms+ogjLsyNYt6hSY5r69P4JQcOPx3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29094c9c57bc20f1ee85988eff7895dccdf0da4cbf342923a0f57e3bd345e737","last_reissued_at":"2026-06-30T01:17:30.609782Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:30.609782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Muhammad Abid, Omer San","submitted_at":"2025-12-09T22:26:29Z","abstract_excerpt":"Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk network, which operates directly on raw spatial or spatiotemporal coordinates through fully connected layers, often struggles to represent sharp gradients, boundary layers, and other non-periodic solution structures on bounded domains. To address these limitations, we introduce the Spectral-Embedded Deep Operator Network (SEDONet), a novel DeepONet architectur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.09165","kind":"arxiv","version":2},"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/2512.09165/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":"2512.09165","created_at":"2026-06-30T01:17:30.609871+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.09165v2","created_at":"2026-06-30T01:17:30.609871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.09165","created_at":"2026-06-30T01:17:30.609871+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEEUZHCXXQQP","created_at":"2026-06-30T01:17:30.609871+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEEUZHCXXQQPD3UF","created_at":"2026-06-30T01:17:30.609871+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEEUZHCX","created_at":"2026-06-30T01:17:30.609871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.24658","citing_title":"WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2605.19076","citing_title":"The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T","json":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T.json","graph_json":"https://pith.science/api/pith-number/FEEUZHCXXQQPD3UFTCHP66EV3T/graph.json","events_json":"https://pith.science/api/pith-number/FEEUZHCXXQQPD3UFTCHP66EV3T/events.json","paper":"https://pith.science/paper/FEEUZHCX"},"agent_actions":{"view_html":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T","download_json":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T.json","view_paper":"https://pith.science/paper/FEEUZHCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.09165&json=true","fetch_graph":"https://pith.science/api/pith-number/FEEUZHCXXQQPD3UFTCHP66EV3T/graph.json","fetch_events":"https://pith.science/api/pith-number/FEEUZHCXXQQPD3UFTCHP66EV3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T/action/storage_attestation","attest_author":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T/action/author_attestation","sign_citation":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T/action/citation_signature","submit_replication":"https://pith.science/pith/FEEUZHCXXQQPD3UFTCHP66EV3T/action/replication_record"}},"created_at":"2026-06-30T01:17:30.609871+00:00","updated_at":"2026-06-30T01:17:30.609871+00:00"}