{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LLDE7RTQVSDTP3GOINH2QMMREP","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":"1d4cf9bac30855f52abb38c70d5b63a3066b847092c9ba68e480d7caedaca559","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T07:08:16Z","title_canon_sha256":"f5a89ae18e70a0ce1192d489728016c05c5ca9c9b0300103bfe7dc2c6713ae69"},"schema_version":"1.0","source":{"id":"2606.31231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31231","created_at":"2026-07-01T01:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31231v1","created_at":"2026-07-01T01:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31231","created_at":"2026-07-01T01:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"LLDE7RTQVSDT","created_at":"2026-07-01T01:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"LLDE7RTQVSDTP3GO","created_at":"2026-07-01T01:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"LLDE7RTQ","created_at":"2026-07-01T01:17:56Z"}],"graph_snapshots":[{"event_id":"sha256:556f18e459befab945aba1e5e1aa324292f1a3f7ac32f5217416373cb3f29dac","target":"graph","created_at":"2026-07-01T01:17:56Z","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/2606.31231/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a rigorous numerical analysis framework for a class of semilinear parabolic problems with nonsmooth initial data. We employ a linear Galerkin finite element method for spatial discretization coupled with a high-order explicit exponential Runge-Kutta (EERK) temporal integration scheme. In contrast to conventional smooth error analysis, the nonsmooth case lacks a priori estimates for the higher-order derivatives of both the nonlinear term and the exact solution. By combining analytic semigroup techniques with fractional power space theory, we establish rigorous bounds for these deriva","authors_text":"Jinwei Fang, Runjie Zhang, Shuo Yang, Zhe Yu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T07:08:16Z","title":"Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31231","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":"sha256:5b39522e3094a149627ff49e03f0845e92a6dfe1e3ffb5055d86c8cf9f09bc99","target":"record","created_at":"2026-07-01T01:17:56Z","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":"1d4cf9bac30855f52abb38c70d5b63a3066b847092c9ba68e480d7caedaca559","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T07:08:16Z","title_canon_sha256":"f5a89ae18e70a0ce1192d489728016c05c5ca9c9b0300103bfe7dc2c6713ae69"},"schema_version":"1.0","source":{"id":"2606.31231","kind":"arxiv","version":1}},"canonical_sha256":"5ac64fc670ac8737ecce434fa8319123e96f3455cb7b700f608ea5260d208ee0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ac64fc670ac8737ecce434fa8319123e96f3455cb7b700f608ea5260d208ee0","first_computed_at":"2026-07-01T01:17:56.387290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:56.387290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NWLWxVlew4oUI+w1WbhOBUPC7NT7S4fikAMtoAmcYRRkqCvIhCRm+zhZah6p4yz+MJnGzaknms4dbzZX8yDxDw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:56.387765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b39522e3094a149627ff49e03f0845e92a6dfe1e3ffb5055d86c8cf9f09bc99","sha256:556f18e459befab945aba1e5e1aa324292f1a3f7ac32f5217416373cb3f29dac"],"state_sha256":"9ceb704e6a39ee707561d9b12f3e7b1166bc0d8aea8dbf6dfa846b709543d6ec"}