{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:244XVQH7XM4JX2RTXQCCPM4WME","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":"16e312cfcf25308ce4a940ee3b55b9ba0cdb29e2c92c95ecf96fcb38356a5857","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-05T17:51:57Z","title_canon_sha256":"c5f63a3a5642273407acb14adfb7d435fb97ead8e5debdb3b5a0edc6215cb1b6"},"schema_version":"1.0","source":{"id":"2210.02432","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.02432","created_at":"2026-07-05T08:23:07Z"},{"alias_kind":"arxiv_version","alias_value":"2210.02432v3","created_at":"2026-07-05T08:23:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.02432","created_at":"2026-07-05T08:23:07Z"},{"alias_kind":"pith_short_12","alias_value":"244XVQH7XM4J","created_at":"2026-07-05T08:23:07Z"},{"alias_kind":"pith_short_16","alias_value":"244XVQH7XM4JX2RT","created_at":"2026-07-05T08:23:07Z"},{"alias_kind":"pith_short_8","alias_value":"244XVQH7","created_at":"2026-07-05T08:23:07Z"}],"graph_snapshots":[{"event_id":"sha256:15c9a37cfa4310b3e77854f04395e8ba4a30247442304e5eff956f6339e15189","target":"graph","created_at":"2026-07-05T08:23:07Z","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/2210.02432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present new second-kind integral-equation formulations of the interior and exterior Dirichlet problems for Laplace's equation. The operators in these formulations are both continuous and coercive on general Lipschitz domains in $\\mathbb{R}^d$, $d\\geq 2$, in the space $L^2(\\Gamma)$, where $\\Gamma$ denotes the boundary of the domain. These properties of continuity and coercivity immediately imply that (i) the Galerkin method converges when applied to these formulations; and (ii) the Galerkin matrices are well-conditioned as the discretisation is refined, without the need for operator precondi","authors_text":"Euan A. Spence, Simon N. Chandler-Wilde","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-05T17:51:57Z","title":"Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.02432","kind":"arxiv","version":3},"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:ba5647fc6e0342058974df8b04c23d68b03f4a2794af752f58124a7a7dcc1adb","target":"record","created_at":"2026-07-05T08:23:07Z","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":"16e312cfcf25308ce4a940ee3b55b9ba0cdb29e2c92c95ecf96fcb38356a5857","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-05T17:51:57Z","title_canon_sha256":"c5f63a3a5642273407acb14adfb7d435fb97ead8e5debdb3b5a0edc6215cb1b6"},"schema_version":"1.0","source":{"id":"2210.02432","kind":"arxiv","version":3}},"canonical_sha256":"d7397ac0ffbb389bea33bc0427b396613ce258591a4deb615fbb48392e5cff78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7397ac0ffbb389bea33bc0427b396613ce258591a4deb615fbb48392e5cff78","first_computed_at":"2026-07-05T08:23:07.280092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:07.280092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqnsuAjCI88cZ/oclfWf7gak8f1hyMQ14D4wh1P1ppPuSbrwpO4UUJLDGbzCYHBkZvCCctF5hc8IVkRimYirDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:07.280546Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.02432","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba5647fc6e0342058974df8b04c23d68b03f4a2794af752f58124a7a7dcc1adb","sha256:15c9a37cfa4310b3e77854f04395e8ba4a30247442304e5eff956f6339e15189"],"state_sha256":"42c5575ce14926fbdb890213ff1b464c3b4d1599a346ce15c6daf8c07682c4bb"}