{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:O23OXZP66UHY7G6SD672F3IHSU","short_pith_number":"pith:O23OXZP6","canonical_record":{"source":{"id":"2105.07737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-17T11:13:19Z","cross_cats_sorted":["cs.NA","math.NA","math.SP"],"title_canon_sha256":"830efd6dc1e7c1b0c466a41731fcbfdb2b86537f68688b86dc6142abebae45ee","abstract_canon_sha256":"332b41b519e72a3fd0761dd80275af4f27fe25162849e550977f413408da4a96"},"schema_version":"1.0"},"canonical_sha256":"76b6ebe5fef50f8f9bd21fbfa2ed07951b3f8945b18a7b7440b4be4bcd5b895a","source":{"kind":"arxiv","id":"2105.07737","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.07737","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"arxiv_version","alias_value":"2105.07737v3","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.07737","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_12","alias_value":"O23OXZP66UHY","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_16","alias_value":"O23OXZP66UHY7G6S","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_8","alias_value":"O23OXZP6","created_at":"2026-07-05T05:36:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:O23OXZP66UHY7G6SD672F3IHSU","target":"record","payload":{"canonical_record":{"source":{"id":"2105.07737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-17T11:13:19Z","cross_cats_sorted":["cs.NA","math.NA","math.SP"],"title_canon_sha256":"830efd6dc1e7c1b0c466a41731fcbfdb2b86537f68688b86dc6142abebae45ee","abstract_canon_sha256":"332b41b519e72a3fd0761dd80275af4f27fe25162849e550977f413408da4a96"},"schema_version":"1.0"},"canonical_sha256":"76b6ebe5fef50f8f9bd21fbfa2ed07951b3f8945b18a7b7440b4be4bcd5b895a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:36:28.985481Z","signature_b64":"9OlXIb8jRH26KuG53PL5y3pQKGXekrYQluLye/9fZUsvS6594flO4BmAo8CoiG7Nc25nokRs1t5KkZ4Ql5fpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76b6ebe5fef50f8f9bd21fbfa2ed07951b3f8945b18a7b7440b4be4bcd5b895a","last_reissued_at":"2026-07-05T05:36:28.985030Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:36:28.985030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.07737","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:36:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dvx+39fH8Via5ccIytegvD38N+pxPuZf7fGeVNg2nT6it6v0cs4rswqVYBVlYx7fU+STFR4qXZV4MZKKi3IpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:48:20.279944Z"},"content_sha256":"d6dac4518ec7c451f842b23af46ac17d74b8ef025a78e1a0b64a9d48e4a100a1","schema_version":"1.0","event_id":"sha256:d6dac4518ec7c451f842b23af46ac17d74b8ef025a78e1a0b64a9d48e4a100a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:O23OXZP66UHY7G6SD672F3IHSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfectly-matched-layer truncation is exponentially accurate at high frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.SP"],"primary_cat":"math.AP","authors_text":"David Lafontaine, Euan A. Spence, Jeffrey Galkowski","submitted_at":"2021-05-17T11:13:19Z","abstract_excerpt":"We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the PML solution is exponentially close, both in frequency and the tangent of the scaling angle, to the true scattering solution. Moreover, for a fixed scaling angle and large enough PML width, the PML solution is exponentially close to the true scattering solution in both frequency and the PML width. In fact, the exponential bound holds with rate of decay $c(w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.07737","kind":"arxiv","version":3},"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/2105.07737/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:36:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1Jp7aQ+HZVViQ+V3Lggw8rjkRLl3kxhqMVrkX5DZD4hKtcORJkJUCT1EYfIixRtaDhQ5ziMZ2YLYlapU94JAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:48:20.280328Z"},"content_sha256":"185d2105b744312ebfc0d70d2415da47fbed94ee18b98a49a0f23296901f2b4d","schema_version":"1.0","event_id":"sha256:185d2105b744312ebfc0d70d2415da47fbed94ee18b98a49a0f23296901f2b4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O23OXZP66UHY7G6SD672F3IHSU/bundle.json","state_url":"https://pith.science/pith/O23OXZP66UHY7G6SD672F3IHSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O23OXZP66UHY7G6SD672F3IHSU/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":"2026-07-06T14:48:20Z","links":{"resolver":"https://pith.science/pith/O23OXZP66UHY7G6SD672F3IHSU","bundle":"https://pith.science/pith/O23OXZP66UHY7G6SD672F3IHSU/bundle.json","state":"https://pith.science/pith/O23OXZP66UHY7G6SD672F3IHSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O23OXZP66UHY7G6SD672F3IHSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:O23OXZP66UHY7G6SD672F3IHSU","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":"332b41b519e72a3fd0761dd80275af4f27fe25162849e550977f413408da4a96","cross_cats_sorted":["cs.NA","math.NA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-17T11:13:19Z","title_canon_sha256":"830efd6dc1e7c1b0c466a41731fcbfdb2b86537f68688b86dc6142abebae45ee"},"schema_version":"1.0","source":{"id":"2105.07737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.07737","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"arxiv_version","alias_value":"2105.07737v3","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.07737","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_12","alias_value":"O23OXZP66UHY","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_16","alias_value":"O23OXZP66UHY7G6S","created_at":"2026-07-05T05:36:28Z"},{"alias_kind":"pith_short_8","alias_value":"O23OXZP6","created_at":"2026-07-05T05:36:28Z"}],"graph_snapshots":[{"event_id":"sha256:185d2105b744312ebfc0d70d2415da47fbed94ee18b98a49a0f23296901f2b4d","target":"graph","created_at":"2026-07-05T05:36:28Z","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/2105.07737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the PML solution is exponentially close, both in frequency and the tangent of the scaling angle, to the true scattering solution. Moreover, for a fixed scaling angle and large enough PML width, the PML solution is exponentially close to the true scattering solution in both frequency and the PML width. In fact, the exponential bound holds with rate of decay $c(w","authors_text":"David Lafontaine, Euan A. Spence, Jeffrey Galkowski","cross_cats":["cs.NA","math.NA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-17T11:13:19Z","title":"Perfectly-matched-layer truncation is exponentially accurate at high frequency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.07737","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:d6dac4518ec7c451f842b23af46ac17d74b8ef025a78e1a0b64a9d48e4a100a1","target":"record","created_at":"2026-07-05T05:36:28Z","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":"332b41b519e72a3fd0761dd80275af4f27fe25162849e550977f413408da4a96","cross_cats_sorted":["cs.NA","math.NA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-17T11:13:19Z","title_canon_sha256":"830efd6dc1e7c1b0c466a41731fcbfdb2b86537f68688b86dc6142abebae45ee"},"schema_version":"1.0","source":{"id":"2105.07737","kind":"arxiv","version":3}},"canonical_sha256":"76b6ebe5fef50f8f9bd21fbfa2ed07951b3f8945b18a7b7440b4be4bcd5b895a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76b6ebe5fef50f8f9bd21fbfa2ed07951b3f8945b18a7b7440b4be4bcd5b895a","first_computed_at":"2026-07-05T05:36:28.985030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:36:28.985030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OlXIb8jRH26KuG53PL5y3pQKGXekrYQluLye/9fZUsvS6594flO4BmAo8CoiG7Nc25nokRs1t5KkZ4Ql5fpCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:36:28.985481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.07737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6dac4518ec7c451f842b23af46ac17d74b8ef025a78e1a0b64a9d48e4a100a1","sha256:185d2105b744312ebfc0d70d2415da47fbed94ee18b98a49a0f23296901f2b4d"],"state_sha256":"9f7474991a1c3afa1dac6c13ffcc1ef2b374435a189163f4514ae60a6bbc8428"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7Za1iPboS78cI9WkDDIidBhfdUyyo1BqcFTdQhPRla6jeMnP7D7xKSXkJ5YRkU1aax1CB1802kwojPXPAPuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:48:20.282220Z","bundle_sha256":"6ef42145133bd33dd2542650a0a84bc34b915e696079ff7118af7716f93f9882"}}