{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YFQ2RBDBOM7RTXSQYJLJ3UP347","short_pith_number":"pith:YFQ2RBDB","canonical_record":{"source":{"id":"2101.11963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-28T12:33:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bfc0d888f4f975340957798c9c90df8722cb1d5da621b67f65f692554d8d861b","abstract_canon_sha256":"b7e191fcddb186a89f8ad1be20a1da5ab59c5380e5cb05105014910a35b8f32b"},"schema_version":"1.0"},"canonical_sha256":"c161a88461733f19de50c2569dd1fbe7c9a26ef647ec0df380658db4a5315139","source":{"kind":"arxiv","id":"2101.11963","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.11963","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2101.11963v2","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.11963","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"YFQ2RBDBOM7R","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"YFQ2RBDBOM7RTXSQ","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"YFQ2RBDB","created_at":"2026-07-05T02:10:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YFQ2RBDBOM7RTXSQYJLJ3UP347","target":"record","payload":{"canonical_record":{"source":{"id":"2101.11963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-28T12:33:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bfc0d888f4f975340957798c9c90df8722cb1d5da621b67f65f692554d8d861b","abstract_canon_sha256":"b7e191fcddb186a89f8ad1be20a1da5ab59c5380e5cb05105014910a35b8f32b"},"schema_version":"1.0"},"canonical_sha256":"c161a88461733f19de50c2569dd1fbe7c9a26ef647ec0df380658db4a5315139","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:10:41.977867Z","signature_b64":"RZjempP5GlO9EjTXbd27hHAWtqgWrgA4ILBLOJOxu3Ni8p7i1L2Kum+M2oQvCbdzIzGSFuV05pjQNgdhqMibAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c161a88461733f19de50c2569dd1fbe7c9a26ef647ec0df380658db4a5315139","last_reissued_at":"2026-07-05T02:10:41.977447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:10:41.977447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.11963","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":"2026-07-05T02:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFE8w0DHjxtovXosxw/K8oOfUkIzUl9H5ibMBWre5UFrTqpLPcK/5e9Fedm++u5GygvYZIh/1xkq0OPbqtsYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:41:55.130746Z"},"content_sha256":"583427b27079dce07fe1f26c17bd675eabf1e1688ae41337a8e30803ce3fae8f","schema_version":"1.0","event_id":"sha256:583427b27079dce07fe1f26c17bd675eabf1e1688ae41337a8e30803ce3fae8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YFQ2RBDBOM7RTXSQYJLJ3UP347","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the computation of recurrence coefficients for univariate orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Akil Narayan, Zexin Liu","submitted_at":"2021-01-28T12:33:09Z","abstract_excerpt":"Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern computational tools that facilitate evaluation and manipulation of polynomials with respect to the measure, and such tasks are foundational in numerical approximation and quadrature. Although the recurrence coefficients for classical measures are known explicitly, those for nonclassical measures must typically be numerically computed. We survey and review exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.11963","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.11963/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":"2026-07-05T02:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zl2oN8PaVUoEoZnMy0TvymrmNjTPvUcUtWyMxIRrWxz0SR2gn+KxFDpbfYZGebb0WOSfJMx5erNJ1xO/W3RlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:41:55.131280Z"},"content_sha256":"f06c958e995d7896b27cc2f51a3e2921fe40e5e06649e71472b631bf2164a0af","schema_version":"1.0","event_id":"sha256:f06c958e995d7896b27cc2f51a3e2921fe40e5e06649e71472b631bf2164a0af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/bundle.json","state_url":"https://pith.science/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/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":"2026-08-03T18:41:55Z","links":{"resolver":"https://pith.science/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347","bundle":"https://pith.science/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/bundle.json","state":"https://pith.science/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFQ2RBDBOM7RTXSQYJLJ3UP347/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YFQ2RBDBOM7RTXSQYJLJ3UP347","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":"b7e191fcddb186a89f8ad1be20a1da5ab59c5380e5cb05105014910a35b8f32b","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-28T12:33:09Z","title_canon_sha256":"bfc0d888f4f975340957798c9c90df8722cb1d5da621b67f65f692554d8d861b"},"schema_version":"1.0","source":{"id":"2101.11963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.11963","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2101.11963v2","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.11963","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"YFQ2RBDBOM7R","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"YFQ2RBDBOM7RTXSQ","created_at":"2026-07-05T02:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"YFQ2RBDB","created_at":"2026-07-05T02:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:f06c958e995d7896b27cc2f51a3e2921fe40e5e06649e71472b631bf2164a0af","target":"graph","created_at":"2026-07-05T02:10:41Z","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/2101.11963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern computational tools that facilitate evaluation and manipulation of polynomials with respect to the measure, and such tasks are foundational in numerical approximation and quadrature. Although the recurrence coefficients for classical measures are known explicitly, those for nonclassical measures must typically be numerically computed. We survey and review exi","authors_text":"Akil Narayan, Zexin Liu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-28T12:33:09Z","title":"On the computation of recurrence coefficients for univariate orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.11963","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":"sha256:583427b27079dce07fe1f26c17bd675eabf1e1688ae41337a8e30803ce3fae8f","target":"record","created_at":"2026-07-05T02:10:41Z","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":"b7e191fcddb186a89f8ad1be20a1da5ab59c5380e5cb05105014910a35b8f32b","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-28T12:33:09Z","title_canon_sha256":"bfc0d888f4f975340957798c9c90df8722cb1d5da621b67f65f692554d8d861b"},"schema_version":"1.0","source":{"id":"2101.11963","kind":"arxiv","version":2}},"canonical_sha256":"c161a88461733f19de50c2569dd1fbe7c9a26ef647ec0df380658db4a5315139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c161a88461733f19de50c2569dd1fbe7c9a26ef647ec0df380658db4a5315139","first_computed_at":"2026-07-05T02:10:41.977447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:10:41.977447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RZjempP5GlO9EjTXbd27hHAWtqgWrgA4ILBLOJOxu3Ni8p7i1L2Kum+M2oQvCbdzIzGSFuV05pjQNgdhqMibAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:10:41.977867Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.11963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:583427b27079dce07fe1f26c17bd675eabf1e1688ae41337a8e30803ce3fae8f","sha256:f06c958e995d7896b27cc2f51a3e2921fe40e5e06649e71472b631bf2164a0af"],"state_sha256":"74b9809cddf81cb6abd3d3d1380954a36056ac07073296f531ccc403d9b68139"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlI/aRuNzzMfsC09QFufbXTFlMg96dkzV+EKLAMAkzna4cOhig9OKQst0TlefIkHt1gjxTUBkCie1vbCxaf8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:41:55.135195Z","bundle_sha256":"0972a209e00df248506203f6af01d7aef2b42165c9b98a4673d4ab62e1cba9df"}}