{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QISXN2LVGXPYLKO7K77RZOC4ZC","short_pith_number":"pith:QISXN2LV","canonical_record":{"source":{"id":"1906.03907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-10T11:32:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"21d8d873d4cfd6d5f7f9a9c03792e5de27cabf75347aa813bc6f54af4c06b558","abstract_canon_sha256":"44e51b8c054fd80cb3da01370e21e161b11656dd57b40687d78a9dad390f22cb"},"schema_version":"1.0"},"canonical_sha256":"822576e97535df85a9df57ff1cb85cc881f539b9beabee0529bd549f18ddfab6","source":{"kind":"arxiv","id":"1906.03907","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03907","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03907v1","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03907","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"QISXN2LVGXPY","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_16","alias_value":"QISXN2LVGXPYLKO7","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_8","alias_value":"QISXN2LV","created_at":"2026-07-05T09:09:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QISXN2LVGXPYLKO7K77RZOC4ZC","target":"record","payload":{"canonical_record":{"source":{"id":"1906.03907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-10T11:32:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"21d8d873d4cfd6d5f7f9a9c03792e5de27cabf75347aa813bc6f54af4c06b558","abstract_canon_sha256":"44e51b8c054fd80cb3da01370e21e161b11656dd57b40687d78a9dad390f22cb"},"schema_version":"1.0"},"canonical_sha256":"822576e97535df85a9df57ff1cb85cc881f539b9beabee0529bd549f18ddfab6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:45.605307Z","signature_b64":"yT86JR+b5+zAo4z9IPeWS3CvlbuZvCCwyfJf7fLaUHtFraI20uZR6VUFRCdwtGG6JOmdWKZowSfXpH8ULGLUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"822576e97535df85a9df57ff1cb85cc881f539b9beabee0529bd549f18ddfab6","last_reissued_at":"2026-07-05T09:09:45.604948Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:45.604948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.03907","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":"2026-07-05T09:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tD2xiklVyUi6Ln4WZjeFYJVn0eJoelf66s1ZQ76J5mg6M/5JRfy50/dcc8YEvjEEXLT6UGRK2i6U213iis+xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:25:22.465122Z"},"content_sha256":"25d690e8a7a5f9b358919a6055d4b1ac2278b3255277815871243d410e8beeec","schema_version":"1.0","event_id":"sha256:25d690e8a7a5f9b358919a6055d4b1ac2278b3255277815871243d410e8beeec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QISXN2LVGXPYLKO7K77RZOC4ZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Sheehan Olver, Timon S. Gutleb","submitted_at":"2019-06-10T11:32:35Z","abstract_excerpt":"We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to achieve high efficiency and exponential convergence. The discussion is followed by a demonstration of the method on example Volterra integral equations of the first and second kind with known analytic solutions as well as an application-oriented numerical experiment. We prove convergence for both first and second kind problems, where the former builds on connecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03907","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.03907/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":"2026-07-05T09:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZGVpViEZZiASBUdRPXt5R2MCHTWJqCkltEv7UqIZk8xNiQny9Xh9Q+tNLsYe1txW1iGwO6C6QJzf389gaoMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:25:22.471596Z"},"content_sha256":"3dac100aacf64a56e82daab29f040774f7b0576de68fdac9278d9db0800efc69","schema_version":"1.0","event_id":"sha256:3dac100aacf64a56e82daab29f040774f7b0576de68fdac9278d9db0800efc69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/bundle.json","state_url":"https://pith.science/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/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":"2026-08-18T14:25:22Z","links":{"resolver":"https://pith.science/pith/QISXN2LVGXPYLKO7K77RZOC4ZC","bundle":"https://pith.science/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/bundle.json","state":"https://pith.science/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QISXN2LVGXPYLKO7K77RZOC4ZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QISXN2LVGXPYLKO7K77RZOC4ZC","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":"44e51b8c054fd80cb3da01370e21e161b11656dd57b40687d78a9dad390f22cb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-10T11:32:35Z","title_canon_sha256":"21d8d873d4cfd6d5f7f9a9c03792e5de27cabf75347aa813bc6f54af4c06b558"},"schema_version":"1.0","source":{"id":"1906.03907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03907","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03907v1","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03907","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"QISXN2LVGXPY","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_16","alias_value":"QISXN2LVGXPYLKO7","created_at":"2026-07-05T09:09:45Z"},{"alias_kind":"pith_short_8","alias_value":"QISXN2LV","created_at":"2026-07-05T09:09:45Z"}],"graph_snapshots":[{"event_id":"sha256:3dac100aacf64a56e82daab29f040774f7b0576de68fdac9278d9db0800efc69","target":"graph","created_at":"2026-07-05T09:09:45Z","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/1906.03907/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to achieve high efficiency and exponential convergence. The discussion is followed by a demonstration of the method on example Volterra integral equations of the first and second kind with known analytic solutions as well as an application-oriented numerical experiment. We prove convergence for both first and second kind problems, where the former builds on connecti","authors_text":"Sheehan Olver, Timon S. Gutleb","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-10T11:32:35Z","title":"A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03907","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":"sha256:25d690e8a7a5f9b358919a6055d4b1ac2278b3255277815871243d410e8beeec","target":"record","created_at":"2026-07-05T09:09:45Z","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":"44e51b8c054fd80cb3da01370e21e161b11656dd57b40687d78a9dad390f22cb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-10T11:32:35Z","title_canon_sha256":"21d8d873d4cfd6d5f7f9a9c03792e5de27cabf75347aa813bc6f54af4c06b558"},"schema_version":"1.0","source":{"id":"1906.03907","kind":"arxiv","version":1}},"canonical_sha256":"822576e97535df85a9df57ff1cb85cc881f539b9beabee0529bd549f18ddfab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"822576e97535df85a9df57ff1cb85cc881f539b9beabee0529bd549f18ddfab6","first_computed_at":"2026-07-05T09:09:45.604948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:45.604948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yT86JR+b5+zAo4z9IPeWS3CvlbuZvCCwyfJf7fLaUHtFraI20uZR6VUFRCdwtGG6JOmdWKZowSfXpH8ULGLUBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:45.605307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.03907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25d690e8a7a5f9b358919a6055d4b1ac2278b3255277815871243d410e8beeec","sha256:3dac100aacf64a56e82daab29f040774f7b0576de68fdac9278d9db0800efc69"],"state_sha256":"47acb4959c3a80907faf4ec3b3521f82857b7e6d39a778543611d6c353ca6040"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfYh4gzjORctNN/viH/TaS8wxSHo1lNbCARmWFIgZlG/GwQ2jgXmpLc4QOkioFgrn81idpie/rbZKCbodFSfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T14:25:22.496935Z","bundle_sha256":"aa85f28463e0a046bf3547fc6a5ddbd73937ae2bc844ebaad0d17fdcb7e53b3b"}}