{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:V2BBC5A7HHTN2TLOCDIV4G7VKD","short_pith_number":"pith:V2BBC5A7","schema_version":"1.0","canonical_sha256":"ae8211741f39e6dd4d6e10d15e1bf550e4b43dae39de4fc6e8dd6217ecf923df","source":{"kind":"arxiv","id":"2312.12547","version":1},"attestation_state":"computed","paper":{"title":"Stable least-squares space-time boundary element methods for the wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Carolina Urz\\'ua-Torres, Daniel Hoonhout, Olaf Steinbach, Richard L\\\"oscher","submitted_at":"2023-12-19T19:34:56Z","abstract_excerpt":"In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\\Sigma)$, where $\\Sigma := \\partial \\Omega \\times (0,T)$ is the lateral boundary of the space-time domain $Q := \\Omega \\times (0,T)$. For discretization, the minimization problem is restated as a mixed saddle point formulation. Unique solvability is established by combining conforming nested boundary element spaces for the mixed formulation such that the related bilinear form is discrete inf-sup stable. We a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2312.12547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-12-19T19:34:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ce6db08ea5865bcbc4ae2d1e2e9fe1c1e39c1251eebdaa72323dae4efc834bc8","abstract_canon_sha256":"4c014da38f10b8bf96ff54897b6ad02cc2cdd99d449a0e2ccff29f9b0c635bba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:26:22.473671Z","signature_b64":"jIghQDe6hH6BPoXOcNDL2GFT0FA+GFg5Ix/yIuD8mMDgrBWt8mgD2ycbHXZ5M7AnqinbWRp2KWyyBpAgPMWKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae8211741f39e6dd4d6e10d15e1bf550e4b43dae39de4fc6e8dd6217ecf923df","last_reissued_at":"2026-07-05T07:26:22.473255Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:26:22.473255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable least-squares space-time boundary element methods for the wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Carolina Urz\\'ua-Torres, Daniel Hoonhout, Olaf Steinbach, Richard L\\\"oscher","submitted_at":"2023-12-19T19:34:56Z","abstract_excerpt":"In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\\Sigma)$, where $\\Sigma := \\partial \\Omega \\times (0,T)$ is the lateral boundary of the space-time domain $Q := \\Omega \\times (0,T)$. For discretization, the minimization problem is restated as a mixed saddle point formulation. Unique solvability is established by combining conforming nested boundary element spaces for the mixed formulation such that the related bilinear form is discrete inf-sup stable. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12547","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/2312.12547/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2312.12547","created_at":"2026-07-05T07:26:22.473311+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.12547v1","created_at":"2026-07-05T07:26:22.473311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12547","created_at":"2026-07-05T07:26:22.473311+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2BBC5A7HHTN","created_at":"2026-07-05T07:26:22.473311+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2BBC5A7HHTN2TLO","created_at":"2026-07-05T07:26:22.473311+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2BBC5A7","created_at":"2026-07-05T07:26:22.473311+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02288","citing_title":"Paving the way to a $\\operatorname{T}$-coercive method for the wave equation","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD","json":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD.json","graph_json":"https://pith.science/api/pith-number/V2BBC5A7HHTN2TLOCDIV4G7VKD/graph.json","events_json":"https://pith.science/api/pith-number/V2BBC5A7HHTN2TLOCDIV4G7VKD/events.json","paper":"https://pith.science/paper/V2BBC5A7"},"agent_actions":{"view_html":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD","download_json":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD.json","view_paper":"https://pith.science/paper/V2BBC5A7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.12547&json=true","fetch_graph":"https://pith.science/api/pith-number/V2BBC5A7HHTN2TLOCDIV4G7VKD/graph.json","fetch_events":"https://pith.science/api/pith-number/V2BBC5A7HHTN2TLOCDIV4G7VKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD/action/storage_attestation","attest_author":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD/action/author_attestation","sign_citation":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD/action/citation_signature","submit_replication":"https://pith.science/pith/V2BBC5A7HHTN2TLOCDIV4G7VKD/action/replication_record"}},"created_at":"2026-07-05T07:26:22.473311+00:00","updated_at":"2026-07-05T07:26:22.473311+00:00"}