{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FWJ4B6BEGWGJ5IAPB5OGOCQIH3","short_pith_number":"pith:FWJ4B6BE","canonical_record":{"source":{"id":"1810.02483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-05T01:27:18Z","cross_cats_sorted":[],"title_canon_sha256":"85ca4a036cb675d6d2293f1f2ee78e422c7c0a747dd8b2fe243cbfe11142dd3f","abstract_canon_sha256":"c762a60b004d332ef83cf6ef26d92d0f414661bd659924da6c6ed9308c976925"},"schema_version":"1.0"},"canonical_sha256":"2d93c0f824358c9ea00f0f5c670a083edff106daa0e523e591171e79137ae075","source":{"kind":"arxiv","id":"1810.02483","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02483","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02483v1","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02483","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"FWJ4B6BEGWGJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FWJ4B6BEGWGJ5IAP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FWJ4B6BE","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FWJ4B6BEGWGJ5IAPB5OGOCQIH3","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-05T01:27:18Z","cross_cats_sorted":[],"title_canon_sha256":"85ca4a036cb675d6d2293f1f2ee78e422c7c0a747dd8b2fe243cbfe11142dd3f","abstract_canon_sha256":"c762a60b004d332ef83cf6ef26d92d0f414661bd659924da6c6ed9308c976925"},"schema_version":"1.0"},"canonical_sha256":"2d93c0f824358c9ea00f0f5c670a083edff106daa0e523e591171e79137ae075","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:01.730139Z","signature_b64":"tS6moC71ZeeCQQviW2/uDkce3FyTAGGCRSeJ8aUKQ4BG1J2I/l/x9ClSLpxUQMC3vO5X2Ag7ITYHykQ4r6LKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d93c0f824358c9ea00f0f5c670a083edff106daa0e523e591171e79137ae075","last_reissued_at":"2026-05-18T00:04:01.729491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:01.729491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02483","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOyXCJKT71e0RLo8aScxAZ0MY/xqqfXlp4V1mMxIxTHtTRv7NecvdGSlNcBslAMD12ZLb1qKVozsIcw0vD9aBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:15:10.962959Z"},"content_sha256":"65eab964130cc041459c2708a74325840da9b55b5044c9f0866821f5beda7090","schema_version":"1.0","event_id":"sha256:65eab964130cc041459c2708a74325840da9b55b5044c9f0866821f5beda7090"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FWJ4B6BEGWGJ5IAPB5OGOCQIH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic approximations for the close evaluation of double-layer potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Arnold D. Kim, Camille Carvalho, Shilpa Khatri","submitted_at":"2018-10-05T01:27:18Z","abstract_excerpt":"When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular integrals. To address this close evaluation problem, we apply an asymptotic analysis of these nearly singular integrals and obtain an asymptotic approximation. We derive the asymptotic approximation for the case of the double-layer potential in two and three dimensions, representing the solution of the interior Dirichlet problem for Laplace's equation. By doing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02483","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1bIskerfsiGkTxDmJjHJgVlAJ2GexoANg3aRsW9RcCcIWVQ3YNo9XNA99F/54fE+dGTBTEWzm5SnQ2hwgwHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:15:10.963303Z"},"content_sha256":"c7c8f7c6d80108c8c95aacd9092bd612a923678b7d8cd858d67b107b649a7297","schema_version":"1.0","event_id":"sha256:c7c8f7c6d80108c8c95aacd9092bd612a923678b7d8cd858d67b107b649a7297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/bundle.json","state_url":"https://pith.science/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T18:15:10Z","links":{"resolver":"https://pith.science/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3","bundle":"https://pith.science/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/bundle.json","state":"https://pith.science/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWJ4B6BEGWGJ5IAPB5OGOCQIH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FWJ4B6BEGWGJ5IAPB5OGOCQIH3","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":"c762a60b004d332ef83cf6ef26d92d0f414661bd659924da6c6ed9308c976925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-05T01:27:18Z","title_canon_sha256":"85ca4a036cb675d6d2293f1f2ee78e422c7c0a747dd8b2fe243cbfe11142dd3f"},"schema_version":"1.0","source":{"id":"1810.02483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02483","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02483v1","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02483","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"FWJ4B6BEGWGJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FWJ4B6BEGWGJ5IAP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FWJ4B6BE","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:c7c8f7c6d80108c8c95aacd9092bd612a923678b7d8cd858d67b107b649a7297","target":"graph","created_at":"2026-05-18T00:04:01Z","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":"When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular integrals. To address this close evaluation problem, we apply an asymptotic analysis of these nearly singular integrals and obtain an asymptotic approximation. We derive the asymptotic approximation for the case of the double-layer potential in two and three dimensions, representing the solution of the interior Dirichlet problem for Laplace's equation. By doing ","authors_text":"Arnold D. Kim, Camille Carvalho, Shilpa Khatri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-05T01:27:18Z","title":"Asymptotic approximations for the close evaluation of double-layer potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02483","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":"sha256:65eab964130cc041459c2708a74325840da9b55b5044c9f0866821f5beda7090","target":"record","created_at":"2026-05-18T00:04:01Z","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":"c762a60b004d332ef83cf6ef26d92d0f414661bd659924da6c6ed9308c976925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-05T01:27:18Z","title_canon_sha256":"85ca4a036cb675d6d2293f1f2ee78e422c7c0a747dd8b2fe243cbfe11142dd3f"},"schema_version":"1.0","source":{"id":"1810.02483","kind":"arxiv","version":1}},"canonical_sha256":"2d93c0f824358c9ea00f0f5c670a083edff106daa0e523e591171e79137ae075","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d93c0f824358c9ea00f0f5c670a083edff106daa0e523e591171e79137ae075","first_computed_at":"2026-05-18T00:04:01.729491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:01.729491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tS6moC71ZeeCQQviW2/uDkce3FyTAGGCRSeJ8aUKQ4BG1J2I/l/x9ClSLpxUQMC3vO5X2Ag7ITYHykQ4r6LKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:01.730139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65eab964130cc041459c2708a74325840da9b55b5044c9f0866821f5beda7090","sha256:c7c8f7c6d80108c8c95aacd9092bd612a923678b7d8cd858d67b107b649a7297"],"state_sha256":"6b9bfd99169966eeb097d90997e8546b03457f29dcd3835d6a9219a781f04dd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Es6ug1KTYpdpCfNXp7CJITj2JCjdEF34TcMzUktdVY9sZtPRBe9gmSc2RAE1nofBiQ9liKi8GiPVsq6HmfzyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:15:10.965420Z","bundle_sha256":"873b006272ed679704b5d1c57866af70020702656d1241c5e69afde89af734dd"}}