{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:P4G36IM7QVVCJOVCR3TQG6HPHW","short_pith_number":"pith:P4G36IM7","schema_version":"1.0","canonical_sha256":"7f0dbf219f856a24baa28ee70378ef3d84cb75b542e26d941318085a1d474a28","source":{"kind":"arxiv","id":"2606.29147","version":1},"attestation_state":"computed","paper":{"title":"Consistent CutPINNs for Convection-Diffusion Equations on Curved Level-Set Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Maneesh Kumar Singh","submitted_at":"2026-06-28T02:04:29Z","abstract_excerpt":"We present an a priori error analysis of consistent-loss PINNs for stationary convection-diffusion equations on curved level-set domains. The standard mean-squared interior loss fails in the convection-dominated regime: the solution develops an $O(\\eps)$ boundary layer in which the pointwise residual grows like $\\eps^{-1}$, so the loss is dominated by the few collocation points inside the layer and leaves the smooth bulk unresolved. We remove this mismatch by penalising the interior residual in a discrete $\\Lp{\\gamma}$ norm with $\\gamma = 1 + 1/\\log\\mtil$, a computable surrogate for the $\\Hmin"},"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":"2606.29147","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-28T02:04:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"46997ba61c2612d523da5bd3c87480f34406c8fc047111038ae4fb18f4524a7b","abstract_canon_sha256":"02e4517ba8f76fad16effafbf260bfbf23033bee517790576edc8e67bfacc809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:54.581036Z","signature_b64":"K9IvdD8pZnwC7BHjaoffkJrJcQz6Lu1SsJJSzNyk7zAjqeT29DoQYYez6EXE8VTvai/PZmYx8exmns9rtCU1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f0dbf219f856a24baa28ee70378ef3d84cb75b542e26d941318085a1d474a28","last_reissued_at":"2026-06-30T01:17:54.580587Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:54.580587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consistent CutPINNs for Convection-Diffusion Equations on Curved Level-Set Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Maneesh Kumar Singh","submitted_at":"2026-06-28T02:04:29Z","abstract_excerpt":"We present an a priori error analysis of consistent-loss PINNs for stationary convection-diffusion equations on curved level-set domains. The standard mean-squared interior loss fails in the convection-dominated regime: the solution develops an $O(\\eps)$ boundary layer in which the pointwise residual grows like $\\eps^{-1}$, so the loss is dominated by the few collocation points inside the layer and leaves the smooth bulk unresolved. We remove this mismatch by penalising the interior residual in a discrete $\\Lp{\\gamma}$ norm with $\\gamma = 1 + 1/\\log\\mtil$, a computable surrogate for the $\\Hmin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29147","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/2606.29147/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":"2606.29147","created_at":"2026-06-30T01:17:54.580659+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29147v1","created_at":"2026-06-30T01:17:54.580659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29147","created_at":"2026-06-30T01:17:54.580659+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4G36IM7QVVC","created_at":"2026-06-30T01:17:54.580659+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4G36IM7QVVCJOVC","created_at":"2026-06-30T01:17:54.580659+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4G36IM7","created_at":"2026-06-30T01:17:54.580659+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/P4G36IM7QVVCJOVCR3TQG6HPHW","json":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW.json","graph_json":"https://pith.science/api/pith-number/P4G36IM7QVVCJOVCR3TQG6HPHW/graph.json","events_json":"https://pith.science/api/pith-number/P4G36IM7QVVCJOVCR3TQG6HPHW/events.json","paper":"https://pith.science/paper/P4G36IM7"},"agent_actions":{"view_html":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW","download_json":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW.json","view_paper":"https://pith.science/paper/P4G36IM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29147&json=true","fetch_graph":"https://pith.science/api/pith-number/P4G36IM7QVVCJOVCR3TQG6HPHW/graph.json","fetch_events":"https://pith.science/api/pith-number/P4G36IM7QVVCJOVCR3TQG6HPHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW/action/storage_attestation","attest_author":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW/action/author_attestation","sign_citation":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW/action/citation_signature","submit_replication":"https://pith.science/pith/P4G36IM7QVVCJOVCR3TQG6HPHW/action/replication_record"}},"created_at":"2026-06-30T01:17:54.580659+00:00","updated_at":"2026-06-30T01:17:54.580659+00:00"}