{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BJQEBY2LEVZONI63IB5THL66HD","short_pith_number":"pith:BJQEBY2L","canonical_record":{"source":{"id":"1810.03835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T06:45:16Z","cross_cats_sorted":[],"title_canon_sha256":"d93b3ec43b521f0f8c18a99197ec8c1a7f4c21157a2c0696536900501ec9c095","abstract_canon_sha256":"8d8c13517fc02aaf712590af39dc7cd8c7ade7208afdb8ade8dd76b122e35c45"},"schema_version":"1.0"},"canonical_sha256":"0a6040e34b2572e6a3db407b33afde38fccbe8b637aab744fd168011ffc7b853","source":{"kind":"arxiv","id":"1810.03835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03835","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03835v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03835","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"BJQEBY2LEVZO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BJQEBY2LEVZONI63","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BJQEBY2L","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BJQEBY2LEVZONI63IB5THL66HD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T06:45:16Z","cross_cats_sorted":[],"title_canon_sha256":"d93b3ec43b521f0f8c18a99197ec8c1a7f4c21157a2c0696536900501ec9c095","abstract_canon_sha256":"8d8c13517fc02aaf712590af39dc7cd8c7ade7208afdb8ade8dd76b122e35c45"},"schema_version":"1.0"},"canonical_sha256":"0a6040e34b2572e6a3db407b33afde38fccbe8b637aab744fd168011ffc7b853","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:44.429918Z","signature_b64":"1uCr1J419wmbx3hoAgf3QZvD2kbVNbu+AxlcB4YKy41ake9Gx38w2MAbb0mP/QhyYfi9CaYuJuMl1BrfzAhgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a6040e34b2572e6a3db407b33afde38fccbe8b637aab744fd168011ffc7b853","last_reissued_at":"2026-05-18T00:03:44.429489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:44.429489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03835","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":"2026-05-18T00:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aX6WxRMXAJfKhK0V+JQQqpIM1B+Znd8kMuacnanMM7DlmBwJqkNqKaWxwuVKLKwJaNTW7QBrPYDUMy7puDrDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:54:28.425360Z"},"content_sha256":"39f013744b56a343382a47a75d1382ca562e33072bfc42a51e95d66aa1d71556","schema_version":"1.0","event_id":"sha256:39f013744b56a343382a47a75d1382ca562e33072bfc42a51e95d66aa1d71556"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BJQEBY2LEVZONI63IB5THL66HD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Fourier extension based numerical integration scheme for fast and high-order approximation of convolutions with weakly singular kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Akash Anand, Awanish Kumar Tiwari","submitted_at":"2018-10-09T06:45:16Z","abstract_excerpt":"Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for numerical solution of integral equations. Most fast techniques in this direction utilize uniform grid discretizations of the integral that facilitate the use of FFT for $O(n\\log n)$ computations on a grid of size $n$. In general, however, the resulting error converges slowly with increasing $n$ when the integrand does not have a smooth periodic extension. Such exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03835","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":"2026-05-18T00:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fp5SkqvtK3/gJ0SELUwqaEFCDaJjyfx6vwFh/lJCn2YyzQX41/Mjz3YmnPg6zpcvuhnPoInnKqrxhHc/DxhrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:54:28.426077Z"},"content_sha256":"b56442c5ec554a15817b072de1e3dcb051c688085989a69e38992a577d331134","schema_version":"1.0","event_id":"sha256:b56442c5ec554a15817b072de1e3dcb051c688085989a69e38992a577d331134"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJQEBY2LEVZONI63IB5THL66HD/bundle.json","state_url":"https://pith.science/pith/BJQEBY2LEVZONI63IB5THL66HD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJQEBY2LEVZONI63IB5THL66HD/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":"2026-06-11T22:54:28Z","links":{"resolver":"https://pith.science/pith/BJQEBY2LEVZONI63IB5THL66HD","bundle":"https://pith.science/pith/BJQEBY2LEVZONI63IB5THL66HD/bundle.json","state":"https://pith.science/pith/BJQEBY2LEVZONI63IB5THL66HD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJQEBY2LEVZONI63IB5THL66HD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BJQEBY2LEVZONI63IB5THL66HD","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":"8d8c13517fc02aaf712590af39dc7cd8c7ade7208afdb8ade8dd76b122e35c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T06:45:16Z","title_canon_sha256":"d93b3ec43b521f0f8c18a99197ec8c1a7f4c21157a2c0696536900501ec9c095"},"schema_version":"1.0","source":{"id":"1810.03835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03835","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03835v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03835","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"BJQEBY2LEVZO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BJQEBY2LEVZONI63","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BJQEBY2L","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:b56442c5ec554a15817b072de1e3dcb051c688085989a69e38992a577d331134","target":"graph","created_at":"2026-05-18T00:03:44Z","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":"Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for numerical solution of integral equations. Most fast techniques in this direction utilize uniform grid discretizations of the integral that facilitate the use of FFT for $O(n\\log n)$ computations on a grid of size $n$. In general, however, the resulting error converges slowly with increasing $n$ when the integrand does not have a smooth periodic extension. Such exten","authors_text":"Akash Anand, Awanish Kumar Tiwari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T06:45:16Z","title":"A Fourier extension based numerical integration scheme for fast and high-order approximation of convolutions with weakly singular kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03835","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":"sha256:39f013744b56a343382a47a75d1382ca562e33072bfc42a51e95d66aa1d71556","target":"record","created_at":"2026-05-18T00:03:44Z","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":"8d8c13517fc02aaf712590af39dc7cd8c7ade7208afdb8ade8dd76b122e35c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T06:45:16Z","title_canon_sha256":"d93b3ec43b521f0f8c18a99197ec8c1a7f4c21157a2c0696536900501ec9c095"},"schema_version":"1.0","source":{"id":"1810.03835","kind":"arxiv","version":1}},"canonical_sha256":"0a6040e34b2572e6a3db407b33afde38fccbe8b637aab744fd168011ffc7b853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6040e34b2572e6a3db407b33afde38fccbe8b637aab744fd168011ffc7b853","first_computed_at":"2026-05-18T00:03:44.429489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:44.429489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1uCr1J419wmbx3hoAgf3QZvD2kbVNbu+AxlcB4YKy41ake9Gx38w2MAbb0mP/QhyYfi9CaYuJuMl1BrfzAhgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:44.429918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39f013744b56a343382a47a75d1382ca562e33072bfc42a51e95d66aa1d71556","sha256:b56442c5ec554a15817b072de1e3dcb051c688085989a69e38992a577d331134"],"state_sha256":"1755ea7dbf618c94de3f0b0453c1f4686f66b90e97fe1f707cbdeda73a395b40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciORpT1m+latI/FmDN3ZEQfkzUrzH3Qwlivk9Y4ARlCdwJbm2V9iXVLAZ3XIPoHpmgXVpKun/VjzmX47EXoeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:54:28.430275Z","bundle_sha256":"36e88b4901dd5d36ce0a8d82ef6f0691140bf23f27d3bb035e0f0961da08bd4c"}}