{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:33PUA2FXMZGMJ7KNIAQUNMIAYM","short_pith_number":"pith:33PUA2FX","canonical_record":{"source":{"id":"1408.3183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-14T02:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"456a4db6ca03ad79b688a556a55ba4e550553a9ef7dc4b2ec2f93910b7791968","abstract_canon_sha256":"0b9776c34ff85f9e5b6adb9999c4f0137b8cd627370bb7766b82d32572c48ddf"},"schema_version":"1.0"},"canonical_sha256":"dedf4068b7664cc4fd4d402146b100c32718bc2c499095406b7c084505798f1c","source":{"kind":"arxiv","id":"1408.3183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3183","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3183v2","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3183","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"pith_short_12","alias_value":"33PUA2FXMZGM","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"33PUA2FXMZGMJ7KN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"33PUA2FX","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:33PUA2FXMZGMJ7KNIAQUNMIAYM","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-14T02:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"456a4db6ca03ad79b688a556a55ba4e550553a9ef7dc4b2ec2f93910b7791968","abstract_canon_sha256":"0b9776c34ff85f9e5b6adb9999c4f0137b8cd627370bb7766b82d32572c48ddf"},"schema_version":"1.0"},"canonical_sha256":"dedf4068b7664cc4fd4d402146b100c32718bc2c499095406b7c084505798f1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:03.712355Z","signature_b64":"lRJ0MZy6MnqgXxQHszvZ9/5wAN9zGzY3n1VfHPEjb2yZ3kz5p0YvGi/uRLMZHK+wU//NlQjyOKplnhPaXQ4MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dedf4068b7664cc4fd4d402146b100c32718bc2c499095406b7c084505798f1c","last_reissued_at":"2026-05-18T02:45:03.711807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:03.711807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3183","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UqZ9mzDaggAxyLzQnEjt44Jb85HyrM9fx7yK7XN/VY9JOfhfJj0Q/G2suU5JRlgaGzonQrZMMuNxjMIHNh5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:19:23.481513Z"},"content_sha256":"10aa8cdbca0aad2d5f6795e7bd343624641e054a675dbee7ba9156659c0869dc","schema_version":"1.0","event_id":"sha256:10aa8cdbca0aad2d5f6795e7bd343624641e054a675dbee7ba9156659c0869dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:33PUA2FXMZGMJ7KNIAQUNMIAYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral equation methods for the Yukawa-Beltrami equation on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bryan Quaife, Mary-Catherine Kropinski, Nilima Nigam","submitted_at":"2014-08-14T02:36:23Z","abstract_excerpt":"An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can be represented by conical functions. Using a suitable representation formula, a Fredholm equation of the second kind with a compact integral operator needs to be solved. The discretization of this integral equation leads to a linear system whose condition number is bounded independent of the size of the system. Several numerical examples exploring the prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3183","kind":"arxiv","version":2},"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":"2026-05-18T02:45:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"it5Wi5o14mFbw9ot/On0UTXmG+GQcvBL9j38TRSn0H0mylQXujl+4HYpLbe0rZJ7tF9pyHXk/+Mnccaaf2fRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:19:23.481868Z"},"content_sha256":"675ccbd455086ba9e927f6c594a67607f330a962744d47d9fc1dab72556b77d5","schema_version":"1.0","event_id":"sha256:675ccbd455086ba9e927f6c594a67607f330a962744d47d9fc1dab72556b77d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/bundle.json","state_url":"https://pith.science/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/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":"2026-05-28T08:19:23Z","links":{"resolver":"https://pith.science/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM","bundle":"https://pith.science/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/bundle.json","state":"https://pith.science/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33PUA2FXMZGMJ7KNIAQUNMIAYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:33PUA2FXMZGMJ7KNIAQUNMIAYM","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":"0b9776c34ff85f9e5b6adb9999c4f0137b8cd627370bb7766b82d32572c48ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-14T02:36:23Z","title_canon_sha256":"456a4db6ca03ad79b688a556a55ba4e550553a9ef7dc4b2ec2f93910b7791968"},"schema_version":"1.0","source":{"id":"1408.3183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3183","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3183v2","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3183","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"pith_short_12","alias_value":"33PUA2FXMZGM","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"33PUA2FXMZGMJ7KN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"33PUA2FX","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:675ccbd455086ba9e927f6c594a67607f330a962744d47d9fc1dab72556b77d5","target":"graph","created_at":"2026-05-18T02:45:03Z","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":"An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can be represented by conical functions. Using a suitable representation formula, a Fredholm equation of the second kind with a compact integral operator needs to be solved. The discretization of this integral equation leads to a linear system whose condition number is bounded independent of the size of the system. Several numerical examples exploring the prope","authors_text":"Bryan Quaife, Mary-Catherine Kropinski, Nilima Nigam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-14T02:36:23Z","title":"Integral equation methods for the Yukawa-Beltrami equation on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3183","kind":"arxiv","version":2},"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":"sha256:10aa8cdbca0aad2d5f6795e7bd343624641e054a675dbee7ba9156659c0869dc","target":"record","created_at":"2026-05-18T02:45:03Z","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":"0b9776c34ff85f9e5b6adb9999c4f0137b8cd627370bb7766b82d32572c48ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-14T02:36:23Z","title_canon_sha256":"456a4db6ca03ad79b688a556a55ba4e550553a9ef7dc4b2ec2f93910b7791968"},"schema_version":"1.0","source":{"id":"1408.3183","kind":"arxiv","version":2}},"canonical_sha256":"dedf4068b7664cc4fd4d402146b100c32718bc2c499095406b7c084505798f1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dedf4068b7664cc4fd4d402146b100c32718bc2c499095406b7c084505798f1c","first_computed_at":"2026-05-18T02:45:03.711807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:03.711807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lRJ0MZy6MnqgXxQHszvZ9/5wAN9zGzY3n1VfHPEjb2yZ3kz5p0YvGi/uRLMZHK+wU//NlQjyOKplnhPaXQ4MDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:03.712355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10aa8cdbca0aad2d5f6795e7bd343624641e054a675dbee7ba9156659c0869dc","sha256:675ccbd455086ba9e927f6c594a67607f330a962744d47d9fc1dab72556b77d5"],"state_sha256":"83521733a255fadacec9f2bf2bc855f64908544e730cee3b38f7a7a6c6f94ad4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JYY8cWoydfYVLVp9Pkrozk/YRB/G0SEwDnA5pKuIk7hwui7LlIZHLx1YJJXg2MHjla4rqQSVMpv7hfIpiwx/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:19:23.483851Z","bundle_sha256":"e3244e27f2a517e47d19a47e6601c50e1eceb399fd2d3bbb02ad275cd07fc0bf"}}