{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LLDE7RTQVSDTP3GOINH2QMMREP","short_pith_number":"pith:LLDE7RTQ","canonical_record":{"source":{"id":"2606.31231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T07:08:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f5a89ae18e70a0ce1192d489728016c05c5ca9c9b0300103bfe7dc2c6713ae69","abstract_canon_sha256":"1d4cf9bac30855f52abb38c70d5b63a3066b847092c9ba68e480d7caedaca559"},"schema_version":"1.0"},"canonical_sha256":"5ac64fc670ac8737ecce434fa8319123e96f3455cb7b700f608ea5260d208ee0","source":{"kind":"arxiv","id":"2606.31231","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LLDE7RTQVSDTP3GOINH2QMMREP","target":"record","payload":{"canonical_record":{"source":{"id":"2606.31231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T07:08:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f5a89ae18e70a0ce1192d489728016c05c5ca9c9b0300103bfe7dc2c6713ae69","abstract_canon_sha256":"1d4cf9bac30855f52abb38c70d5b63a3066b847092c9ba68e480d7caedaca559"},"schema_version":"1.0"},"canonical_sha256":"5ac64fc670ac8737ecce434fa8319123e96f3455cb7b700f608ea5260d208ee0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:56.387765Z","signature_b64":"NWLWxVlew4oUI+w1WbhOBUPC7NT7S4fikAMtoAmcYRRkqCvIhCRm+zhZah6p4yz+MJnGzaknms4dbzZX8yDxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac64fc670ac8737ecce434fa8319123e96f3455cb7b700f608ea5260d208ee0","last_reissued_at":"2026-07-01T01:17:56.387290Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:56.387290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.31231","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7z07bHExQ5h/0iCFSjBt/WzeXlqbo20e1PkvDPVu0nI/CI0raiyKWkoFQlIODa5CUAtkkVorFknBY54wroDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:56:13.163216Z"},"content_sha256":"5b39522e3094a149627ff49e03f0845e92a6dfe1e3ffb5055d86c8cf9f09bc99","schema_version":"1.0","event_id":"sha256:5b39522e3094a149627ff49e03f0845e92a6dfe1e3ffb5055d86c8cf9f09bc99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LLDE7RTQVSDTP3GOINH2QMMREP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jinwei Fang, Runjie Zhang, Shuo Yang, Zhe Yu","submitted_at":"2026-06-30T07:08:16Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31231","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/2606.31231/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBILDxUauwuKpo+rgtCFxGYCB4uVAjd6vitIUKV4wjOGmRv0G7VwvcMdYxQwx4t6Q4Vjz77rp+XDszKbvtJ5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:56:13.163614Z"},"content_sha256":"556f18e459befab945aba1e5e1aa324292f1a3f7ac32f5217416373cb3f29dac","schema_version":"1.0","event_id":"sha256:556f18e459befab945aba1e5e1aa324292f1a3f7ac32f5217416373cb3f29dac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLDE7RTQVSDTP3GOINH2QMMREP/bundle.json","state_url":"https://pith.science/pith/LLDE7RTQVSDTP3GOINH2QMMREP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLDE7RTQVSDTP3GOINH2QMMREP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T09:56:13Z","links":{"resolver":"https://pith.science/pith/LLDE7RTQVSDTP3GOINH2QMMREP","bundle":"https://pith.science/pith/LLDE7RTQVSDTP3GOINH2QMMREP/bundle.json","state":"https://pith.science/pith/LLDE7RTQVSDTP3GOINH2QMMREP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLDE7RTQVSDTP3GOINH2QMMREP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnrws6ReteiKBFnjezpzN4v3NYBWHl+gXCSA+EhCrYO+DCe84crRQT/RTEAwZ+nhWdVs0rhKxUowW53L4Y4TDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T09:56:13.166262Z","bundle_sha256":"bb39bb0e8082d39eb1d7835cf2a9e4906d053e49b75051ab04eceaa9ee109854"}}