{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OUYPLSBAWOITXTVD7HIRKNQFY4","short_pith_number":"pith:OUYPLSBA","canonical_record":{"source":{"id":"1612.00977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T15:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"516c15f6ff73a860576f2bcd11de2107f4df8b9d029fa65e34aeb1482e0ce44e","abstract_canon_sha256":"8aaf67d2967ae3131bd37388b85476ba0963668bd234b86212469633d550fd15"},"schema_version":"1.0"},"canonical_sha256":"7530f5c820b3913bcea3f9d1153605c73d6e276dcdb9e58697d83f053e628a32","source":{"kind":"arxiv","id":"1612.00977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00977","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00977v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00977","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"OUYPLSBAWOIT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OUYPLSBAWOITXTVD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OUYPLSBA","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OUYPLSBAWOITXTVD7HIRKNQFY4","target":"record","payload":{"canonical_record":{"source":{"id":"1612.00977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T15:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"516c15f6ff73a860576f2bcd11de2107f4df8b9d029fa65e34aeb1482e0ce44e","abstract_canon_sha256":"8aaf67d2967ae3131bd37388b85476ba0963668bd234b86212469633d550fd15"},"schema_version":"1.0"},"canonical_sha256":"7530f5c820b3913bcea3f9d1153605c73d6e276dcdb9e58697d83f053e628a32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:53.673772Z","signature_b64":"k2lfW7R67b9GTR9SvSL9x7DNB4L1sjoJfYZkSJwCw/dMqpmOqMGFotmZX6dALoXoOp+1AhvcziT6KIyHvZo7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7530f5c820b3913bcea3f9d1153605c73d6e276dcdb9e58697d83f053e628a32","last_reissued_at":"2026-05-18T00:55:53.673191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:53.673191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.00977","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":"2026-05-18T00:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tX/fmaNkqn97lGRl+jbc+sDSmPrMXOPxBQEKhbgnzevD36KQEaX4RdEJTjt28sqw9m/svGXrxm/g45v9Fp57Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:02:12.393624Z"},"content_sha256":"f63a7fb52f211a39339fe7f06f77df432ab16e53e9a67d9b50d27c9263d16c72","schema_version":"1.0","event_id":"sha256:f63a7fb52f211a39339fe7f06f77df432ab16e53e9a67d9b50d27c9263d16c72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OUYPLSBAWOITXTVD7HIRKNQFY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ubiquitous evaluation of layer potentials using Quadrature by Kernel-Independent Expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Abtin Rahimian, Alex Barnett, Denis Zorin","submitted_at":"2016-12-03T15:52:25Z","abstract_excerpt":"We introduce a quadrature scheme--QBKIX--for the high-order accurate evaluation of layer potentials associated with general elliptic PDEs near to and on the domain boundary. Relying solely on point evaluations of the underlying kernel, our scheme is essentially PDE-independent; in particular, no analytic expansion nor addition theorem is required. Moreover, it applies to boundary integrals with singular, weakly singular, and hypersingular kernels.\n  Our work builds upon Quadrature by Expansion (QBX), which approximates the potential by an analytic expansion in the neighborhood of each expansio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00977","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":"2026-05-18T00:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIdleDVPlUhswgO8dwf9AOiZL0xdDH2aWsDWhuINVCDB0UeHHqzDWBtcNOxwMcHIeWfx+/KJSspiWo72pWEfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:02:12.394221Z"},"content_sha256":"dadbd791d6dc7fd73b03264a7acebeb7efe5c7b2c587efe4bbfa7dffc80709ef","schema_version":"1.0","event_id":"sha256:dadbd791d6dc7fd73b03264a7acebeb7efe5c7b2c587efe4bbfa7dffc80709ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/bundle.json","state_url":"https://pith.science/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/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":"2026-05-22T12:02:12Z","links":{"resolver":"https://pith.science/pith/OUYPLSBAWOITXTVD7HIRKNQFY4","bundle":"https://pith.science/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/bundle.json","state":"https://pith.science/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUYPLSBAWOITXTVD7HIRKNQFY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OUYPLSBAWOITXTVD7HIRKNQFY4","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":"8aaf67d2967ae3131bd37388b85476ba0963668bd234b86212469633d550fd15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T15:52:25Z","title_canon_sha256":"516c15f6ff73a860576f2bcd11de2107f4df8b9d029fa65e34aeb1482e0ce44e"},"schema_version":"1.0","source":{"id":"1612.00977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00977","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00977v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00977","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"OUYPLSBAWOIT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OUYPLSBAWOITXTVD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OUYPLSBA","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:dadbd791d6dc7fd73b03264a7acebeb7efe5c7b2c587efe4bbfa7dffc80709ef","target":"graph","created_at":"2026-05-18T00:55:53Z","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":"We introduce a quadrature scheme--QBKIX--for the high-order accurate evaluation of layer potentials associated with general elliptic PDEs near to and on the domain boundary. Relying solely on point evaluations of the underlying kernel, our scheme is essentially PDE-independent; in particular, no analytic expansion nor addition theorem is required. Moreover, it applies to boundary integrals with singular, weakly singular, and hypersingular kernels.\n  Our work builds upon Quadrature by Expansion (QBX), which approximates the potential by an analytic expansion in the neighborhood of each expansio","authors_text":"Abtin Rahimian, Alex Barnett, Denis Zorin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T15:52:25Z","title":"Ubiquitous evaluation of layer potentials using Quadrature by Kernel-Independent Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00977","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:f63a7fb52f211a39339fe7f06f77df432ab16e53e9a67d9b50d27c9263d16c72","target":"record","created_at":"2026-05-18T00:55:53Z","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":"8aaf67d2967ae3131bd37388b85476ba0963668bd234b86212469633d550fd15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T15:52:25Z","title_canon_sha256":"516c15f6ff73a860576f2bcd11de2107f4df8b9d029fa65e34aeb1482e0ce44e"},"schema_version":"1.0","source":{"id":"1612.00977","kind":"arxiv","version":1}},"canonical_sha256":"7530f5c820b3913bcea3f9d1153605c73d6e276dcdb9e58697d83f053e628a32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7530f5c820b3913bcea3f9d1153605c73d6e276dcdb9e58697d83f053e628a32","first_computed_at":"2026-05-18T00:55:53.673191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:53.673191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k2lfW7R67b9GTR9SvSL9x7DNB4L1sjoJfYZkSJwCw/dMqpmOqMGFotmZX6dALoXoOp+1AhvcziT6KIyHvZo7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:53.673772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f63a7fb52f211a39339fe7f06f77df432ab16e53e9a67d9b50d27c9263d16c72","sha256:dadbd791d6dc7fd73b03264a7acebeb7efe5c7b2c587efe4bbfa7dffc80709ef"],"state_sha256":"af4e89e64cfea9ab03f71f7146101f5fdb6fb55fa0c7c57aa964f63262b5c0a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zESGC2Gnr7DPDVcrZWW6fH4rKrfqm2YGp8m9/cuTyenQVP2o2fYr5g3KM9uVGmJSxcBIRciLVKfCTwwEv0NzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T12:02:12.397002Z","bundle_sha256":"ef262c7b96a75a104664279af587e5ccbb0be5c3daffb1ce5fa7496b0a550d7a"}}