{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RATJ2S37TPDYV2KYJWRIWAV3NQ","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":"d2de7a563d1d388c0ba3f78ad137799e32abb09e68a5537200578b465e4bf905","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-03T22:36:34Z","title_canon_sha256":"512077a6495ebdf9cec869591c4511ca950fa1356c9b2c10e9c5cf4f0fdec554"},"schema_version":"1.0","source":{"id":"2507.03206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03206","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03206v1","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03206","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"RATJ2S37TPDY","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_16","alias_value":"RATJ2S37TPDYV2KY","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_8","alias_value":"RATJ2S37","created_at":"2026-07-05T11:31:54Z"}],"graph_snapshots":[{"event_id":"sha256:15e587cffe8f0ae3d7f856ef468f74c5872e518f759ec9f9396448d7434d1ed9","target":"graph","created_at":"2026-07-05T11:31:54Z","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/2507.03206/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions.\n  In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creat","authors_text":"April Tran, David Bortz","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-03T22:36:34Z","title":"Weak Form Scientific Machine Learning: Test Function Construction for System Identification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03206","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":"sha256:8755eb6e7900a45ba3572a388586eda2caf5696572e160b301c705262cf5ba14","target":"record","created_at":"2026-07-05T11:31:54Z","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":"d2de7a563d1d388c0ba3f78ad137799e32abb09e68a5537200578b465e4bf905","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-03T22:36:34Z","title_canon_sha256":"512077a6495ebdf9cec869591c4511ca950fa1356c9b2c10e9c5cf4f0fdec554"},"schema_version":"1.0","source":{"id":"2507.03206","kind":"arxiv","version":1}},"canonical_sha256":"88269d4b7f9bc78ae9584da28b02bb6c1b0823cb13ea7779e0b6cfa47ca8e11d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88269d4b7f9bc78ae9584da28b02bb6c1b0823cb13ea7779e0b6cfa47ca8e11d","first_computed_at":"2026-07-05T11:31:54.690184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:54.690184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IaEiB37fkpSbkRz1g+xTfn8afyy+ushD6a2/a01ltDcF81qRWfrbmJ+4/R7cZZ6d1qDgm101Gyo+KBCCszbhCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:54.690709Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.03206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8755eb6e7900a45ba3572a388586eda2caf5696572e160b301c705262cf5ba14","sha256:15e587cffe8f0ae3d7f856ef468f74c5872e518f759ec9f9396448d7434d1ed9"],"state_sha256":"c54bc0a516d830253a04c963eca8e8f66044dd3b10896ea7ff7022130e095f11"}