{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VIOOXX4XMEOFS22FND67UZUDLS","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":"641dcd9be8ffa3c1be25035bda2e4dd25a1c0ed9ec62e2d4cce81c0ec9cec207","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-06-03T07:33:27Z","title_canon_sha256":"4ed414c7cded141b13797d683861e38543fe509887f041b208ae842ff734fc48"},"schema_version":"1.0","source":{"id":"2106.01646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.01646","created_at":"2026-07-05T02:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"2106.01646v1","created_at":"2026-07-05T02:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01646","created_at":"2026-07-05T02:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"VIOOXX4XMEOF","created_at":"2026-07-05T02:45:54Z"},{"alias_kind":"pith_short_16","alias_value":"VIOOXX4XMEOFS22F","created_at":"2026-07-05T02:45:54Z"},{"alias_kind":"pith_short_8","alias_value":"VIOOXX4X","created_at":"2026-07-05T02:45:54Z"}],"graph_snapshots":[{"event_id":"sha256:771b7b5dd7ee8cd89971432d05b2d366c05848c6621a58857f4d94f43a381acd","target":"graph","created_at":"2026-07-05T02:45:54Z","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/2106.01646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation in $L^2$, but it also turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation. Instead of the time derivative in the energetic formulation, we use a modified Hilbert transformation, which allows us to stay in Sobolev spaces of the same order. This results in the applicability of stan","authors_text":"Carolina Urz\\'ua-Torres, Marco Zank, Olaf Steinbach","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-06-03T07:33:27Z","title":"Towards coercive boundary element methods for the wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01646","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":"sha256:18dd3aec39c6900da9a9496230b2f55e81be73112de447c25246fa091cfe1e66","target":"record","created_at":"2026-07-05T02:45:54Z","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":"641dcd9be8ffa3c1be25035bda2e4dd25a1c0ed9ec62e2d4cce81c0ec9cec207","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-06-03T07:33:27Z","title_canon_sha256":"4ed414c7cded141b13797d683861e38543fe509887f041b208ae842ff734fc48"},"schema_version":"1.0","source":{"id":"2106.01646","kind":"arxiv","version":1}},"canonical_sha256":"aa1cebdf97611c596b4568fdfa66835cb21c2f31db02d6e90a85001c5cc6d627","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa1cebdf97611c596b4568fdfa66835cb21c2f31db02d6e90a85001c5cc6d627","first_computed_at":"2026-07-05T02:45:54.115305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:45:54.115305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mehY/5eD8+GwUhslaCi4nLOcIwmsysIDyp+2x2MJ/sdqF+9UZdTg72wE4PHCEKQVUV3/KhH4dR3RHg3h8HxYCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:45:54.115738Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.01646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18dd3aec39c6900da9a9496230b2f55e81be73112de447c25246fa091cfe1e66","sha256:771b7b5dd7ee8cd89971432d05b2d366c05848c6621a58857f4d94f43a381acd"],"state_sha256":"05967a27821f07515152a7bdeb08d67fc59a7e4bcc11cf04dc5dfd57a2b09769"}