{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AIUZVPVOPDN5XJZI2X47T2KAG6","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":"cde7673a02220302af8712fd3aa4b83e92b8dc90548f2fac4949b8940ec1c5cb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T15:30:55Z","title_canon_sha256":"2ac49239b9b355bbab14427255e38323b38209f360991dc254fdf751b0040224"},"schema_version":"1.0","source":{"id":"1904.07761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07761","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07761v1","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07761","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"AIUZVPVOPDN5","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AIUZVPVOPDN5XJZI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AIUZVPVO","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9f2d653031c1a61e1eccee44bee14d3aa79245e97c554d9abcfc6835bdae5605","target":"graph","created_at":"2026-05-17T23:48:24Z","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"},"paper":{"abstract_excerpt":"We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity of mixed approximations.\n  Our aim is to have well-posed (ultraweak) formulations that assume low regularity, under the condition of an $L_2$ right-hand side function. We pursue two ways of defining traces and corresponding integration-by-parts formulas. In one case one obtains a non-closed space. This can be fixed by switching to the Kirchh","authors_text":"Alexander Haberl, Norbert Heuer, Thomas F\\\"uhrer","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T15:30:55Z","title":"Trace operators of the bi-Laplacian and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07761","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":"sha256:3268ee2bf07b8d0aaf89f183c2b9106e49ac1e077958828ef2ff2c0fe8999561","target":"record","created_at":"2026-05-17T23:48:24Z","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":"cde7673a02220302af8712fd3aa4b83e92b8dc90548f2fac4949b8940ec1c5cb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T15:30:55Z","title_canon_sha256":"2ac49239b9b355bbab14427255e38323b38209f360991dc254fdf751b0040224"},"schema_version":"1.0","source":{"id":"1904.07761","kind":"arxiv","version":1}},"canonical_sha256":"02299abeae78dbdba728d5f9f9e940379f677add46cbe0dcd1407d5488d5a66c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02299abeae78dbdba728d5f9f9e940379f677add46cbe0dcd1407d5488d5a66c","first_computed_at":"2026-05-17T23:48:24.302678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:24.302678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"65IhwgePtp356RgSFKs8NYDDVENLYxuPJpdHpwtI6G2lhL91GnOAqD2RSuUJVuSJh5SQoOPO0DsjzPeblvewBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:24.303278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3268ee2bf07b8d0aaf89f183c2b9106e49ac1e077958828ef2ff2c0fe8999561","sha256:9f2d653031c1a61e1eccee44bee14d3aa79245e97c554d9abcfc6835bdae5605"],"state_sha256":"42d5b3ac023ba1511754d3763de364d4ec00f7853d9a5cf64763492f4f9bb8fd"}