{"schema_version":"papers/paper-detail-v1","title":"Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees","surface":"papers","opportunity_kernel":{"paper_id":"c9e5a45f-299f-4eda-86ec-7bc22c823158","title":"Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees","authors":["Amartya Mukherjee","Maxwell Fitzsimmons","David C. Del Rey Fernández","Jun Liu"],"arxiv_id":"2603.19165v1","doi":null,"published_at":"2026-03-19T17:19:48.000Z","score_object":{"overall":{"value":3,"scale":"0-10","confidence":0.85,"confidence_reason":"Backfilled from persisted papers.viability_score.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-05-02T02:30:40.136Z","is_stale":true,"source_count":1,"missingness":[]},"technical":{"value":0,"scale":"0-10","confidence":0.15,"confidence_reason":"No persisted technical score source was available; marked low confidence.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-04-16T02:30:40.136Z","is_stale":true,"source_count":0,"missingness":["reproducibility_results.reproducibility_score","deployability_scores.score","paper_extraction_scorecards.reconstruction_score"]},"commercial":{"value":0,"scale":"0-10","confidence":0.75,"confidence_reason":"Backfilled from persisted commercial_flags and repo availability.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-05-02T02:30:40.136Z","is_stale":true,"source_count":1,"missingness":[]},"market":{"value":0,"scale":"0-10","confidence":0.15,"confidence_reason":"No persisted distribution_readiness_scores row was available; marked low confidence.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-04-16T02:30:40.136Z","is_stale":true,"source_count":0,"missingness":["distribution_readiness_scores.score"]},"team":{"value":10,"scale":"0-10","confidence":0.15,"confidence_reason":"No persisted team-quality evidence was available; marked low confidence.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-04-16T02:30:40.136Z","is_stale":true,"source_count":0,"missingness":["engineer_profiles.builder_score","author_startups"]},"methodology":{"value":0,"scale":"0-10","confidence":0.15,"confidence_reason":"No persisted methodology score source was available; marked low confidence.","model_version":"phase0-backfill-v1","pipeline_version":"phase0-kernel-v1","computed_at":"2026-04-02T02:30:40.136Z","fresh_until":"2026-05-02T02:30:40.136Z","is_stale":true,"source_count":0,"missingness":["paper_extraction_scorecards.total_score","paper_extraction_scorecards.standard_extraction_score"]}},"evidence_receipt":{"freshness":"stale","proof_status":"unverified","repo_status":"missing","references_count":0,"source_count":0,"coverage":0.1667,"missingness":["repo_url","references","proof_status","distribution_readiness_scores","paper_extraction_scorecards"],"unresolved_unknowns":["distribution readiness has not been computed yet","proof verification has not been recorded yet"],"last_verification_at":"2026-04-02T02:30:40.136Z"},"lineage_hash":"17d1835129e562845685a877d1e15fc4f335f898f7515896766d9155ec17f1f4"},"distribution":null,"replication_evidence":[],"author_dna":[]}