{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PB3FF3ON56ZBBWNYUC3CV4YFTT","merge_version":"pith-open-graph-merge-v1","event_count":7,"valid_event_count":7,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"095e71412e69dc222b6cf7e8919d8d84d0275c9de852b0aa0b86445dd75a93ec","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-23T19:05:46Z","title_canon_sha256":"505ec0e912291eeba5ed84ad2a4cad48aa7aa5a845d66b6be8da924dc80cc96d"},"schema_version":"1.0","source":{"id":"2607.21753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21753","created_at":"2026-07-27T00:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21753v1","created_at":"2026-07-27T00:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21753","created_at":"2026-07-27T00:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"PB3FF3ON56ZB","created_at":"2026-07-27T00:20:19Z"},{"alias_kind":"pith_short_16","alias_value":"PB3FF3ON56ZBBWNY","created_at":"2026-07-27T00:20:19Z"},{"alias_kind":"pith_short_8","alias_value":"PB3FF3ON","created_at":"2026-07-27T00:20:19Z"}],"graph_snapshots":[{"event_id":"sha256:d88024811897251f33837b09442b04b8d9caec4e83424d1980080d8cbb875734","target":"graph","created_at":"2026-07-27T00:20:19Z","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/2607.21753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose an r-adaptive neural algorithm for Isogeometric Analysis (IGA) based on residual minimization. The boundary-value problem is solved using a standard conforming Galerkin formulation, while a neural network relocates the interior knots. A strong-form residual in the sense of physics-informed neural networks (PINNs) controls a norm stronger than the energy (H^1) error. We therefore weight it by classical a posteriori theory: element residuals scaled by the local mesh size, interface flux jumps, and Neumann boundary residuals yield a computable estimator of the energy error, which we mi","authors_text":"David Pardo, El\\'ias Caru, Judit Mu\\~noz-Matute","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-23T19:05:46Z","title":"Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21753","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:af5e23a735ea8283504cb4b74d8c08f10621f109fdd455db2f244a7bd761bc61","target":"record","created_at":"2026-07-27T00:20:19Z","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":"095e71412e69dc222b6cf7e8919d8d84d0275c9de852b0aa0b86445dd75a93ec","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-23T19:05:46Z","title_canon_sha256":"505ec0e912291eeba5ed84ad2a4cad48aa7aa5a845d66b6be8da924dc80cc96d"},"schema_version":"1.0","source":{"id":"2607.21753","kind":"arxiv","version":1}},"canonical_sha256":"787652edcdefb210d9b8a0b62af3059cec9327494b2393346ca2d15006bdde5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"787652edcdefb210d9b8a0b62af3059cec9327494b2393346ca2d15006bdde5a","first_computed_at":"2026-07-27T00:20:19.234042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T00:20:19.234042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tg1kUDzt8nxJX1JBLChVSNShavCisHbTQoLo6v9LfvxIlBxzOuUQda2Iz9nNbyltk+U1SJBgbvE50W7kUO4Cw==","signature_status":"signed_v1","signed_at":"2026-07-27T00:20:19.234851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21753","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:3665ede4c7633b856b124c925ac12564dbd3f912afb5ac6e3cda86cc7cd273fd","sha256:464ea5c7b5232ef180db8ae70398713c01dfa5b6294f2ecea9f65d23f2fdb1c0","sha256:640cef73cf5ff5535a032fafb4a3145bc6049e6150a4110661f48af834b23408","sha256:7b06bd92a722081550befe9861c138f8cdadb94785f84ec51a7e4d2484ba0a56","sha256:cde5ded3be7fd51bb8bf8bf9424ed4704fc91b379fa7854133686b607402c7ef"]}],"invalid_events":[],"applied_event_ids":["sha256:af5e23a735ea8283504cb4b74d8c08f10621f109fdd455db2f244a7bd761bc61","sha256:d88024811897251f33837b09442b04b8d9caec4e83424d1980080d8cbb875734"],"state_sha256":"2d363fb983f72dc938807cbc1df8d41500e404942959222ce7bc4d509f10e310"}