{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SIHOCY46CSQ5NUCDFG6BJI3BW4","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":"17c974ac9f26726b240cdf86544e9f62ce1f1e2a3474d05be0027e9a58faf78f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-26T05:19:59Z","title_canon_sha256":"75181a1da12358202b4e50335452eb27d8301285b2bb5a0f4e22f250b4104f3e"},"schema_version":"1.0","source":{"id":"2606.27728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27728","created_at":"2026-06-29T01:14:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27728v1","created_at":"2026-06-29T01:14:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27728","created_at":"2026-06-29T01:14:46Z"},{"alias_kind":"pith_short_12","alias_value":"SIHOCY46CSQ5","created_at":"2026-06-29T01:14:46Z"},{"alias_kind":"pith_short_16","alias_value":"SIHOCY46CSQ5NUCD","created_at":"2026-06-29T01:14:46Z"},{"alias_kind":"pith_short_8","alias_value":"SIHOCY46","created_at":"2026-06-29T01:14:46Z"}],"graph_snapshots":[{"event_id":"sha256:8117d99894da2461441cc68014246e0f4fa34216e5c0a6c8fe9739ef4096bfd3","target":"graph","created_at":"2026-06-29T01:14:46Z","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/2606.27728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study hp approximation and additive Schwarz decompositions for variable-order cubical finite element spaces on one-irregular meshes. For fitted homogeneous diffusion interface problems on one-irregular hexahedral meshes, we prove an hp-optimal energy-norm estimate for the interior penalty DG method. The interpolation input is a conforming hp interpolant obtained from fitted conforming closures of one-irregular vertex patches. We also derive stable decompositions for conforming and DG spaces. On one-irregular quadrilateral meshes the bounds allow locally comparable variable polynomial degree","authors_text":"Situan Li, Weiying Zheng","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-26T05:19:59Z","title":"hp-Optimal DG Approximation and Robust Schwarz Decompositions on One-Irregular Cubical Meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27728","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:a9b45f3a2498a4931072958aa96a9a35b27933c3263bdc7d1012596223cfc260","target":"record","created_at":"2026-06-29T01:14:46Z","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":"17c974ac9f26726b240cdf86544e9f62ce1f1e2a3474d05be0027e9a58faf78f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-26T05:19:59Z","title_canon_sha256":"75181a1da12358202b4e50335452eb27d8301285b2bb5a0f4e22f250b4104f3e"},"schema_version":"1.0","source":{"id":"2606.27728","kind":"arxiv","version":1}},"canonical_sha256":"920ee1639e14a1d6d04329bc14a361b70c109ef4447eda4cfc8d4ba805c63e57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920ee1639e14a1d6d04329bc14a361b70c109ef4447eda4cfc8d4ba805c63e57","first_computed_at":"2026-06-29T01:14:46.639690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:14:46.639690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ilw11V4Oqu2UqwXlffpQWceheZe4Tn1SqDQCLQb6BUQ/xjHMXtq4ot8fKGgbFei3AxquKXNIgJtYckQmID5DAg==","signature_status":"signed_v1","signed_at":"2026-06-29T01:14:46.640150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9b45f3a2498a4931072958aa96a9a35b27933c3263bdc7d1012596223cfc260","sha256:8117d99894da2461441cc68014246e0f4fa34216e5c0a6c8fe9739ef4096bfd3"],"state_sha256":"e118ffd3611da58daee5e5b140fe9e98784f6f02d8bafb64f972895e5f0c187b"}