{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QU3GL343XPM2LCTLIV6PHAD3OL","short_pith_number":"pith:QU3GL343","canonical_record":{"source":{"id":"1812.02196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-05T19:25:27Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.SP"],"title_canon_sha256":"556a802a8f4d7a189f1ce8d434c3adafa3ce4ebcfce26476cba1d32efe3b2299","abstract_canon_sha256":"a526ed4bca77ab4b5b9a817c151fe818f7c28830ce5c73f2bbe8de55c9a8dfce"},"schema_version":"1.0"},"canonical_sha256":"853665ef9bbbd9a58a6b457cf3807b72cf49fbeeea7225e58cb6ea8e8deaae46","source":{"kind":"arxiv","id":"1812.02196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02196","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02196v1","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02196","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"QU3GL343XPM2","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QU3GL343XPM2LCTL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QU3GL343","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QU3GL343XPM2LCTLIV6PHAD3OL","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-05T19:25:27Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.SP"],"title_canon_sha256":"556a802a8f4d7a189f1ce8d434c3adafa3ce4ebcfce26476cba1d32efe3b2299","abstract_canon_sha256":"a526ed4bca77ab4b5b9a817c151fe818f7c28830ce5c73f2bbe8de55c9a8dfce"},"schema_version":"1.0"},"canonical_sha256":"853665ef9bbbd9a58a6b457cf3807b72cf49fbeeea7225e58cb6ea8e8deaae46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:47.063985Z","signature_b64":"IJqVyI0YcDpjr5EwLtifzgCxSvd/RqVTWc+JvQTYYUGOtVv/jhQiLgZFWPJU0oC/UTNWANXaGnKjAyF1/Qt9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853665ef9bbbd9a58a6b457cf3807b72cf49fbeeea7225e58cb6ea8e8deaae46","last_reissued_at":"2026-05-17T23:58:47.063628Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:47.063628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02196","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":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Rfu7dwBli27ywv+JwpOWrdFcEupzrOkbNsxIBLm5Y1bgRbiB8uVUOt9RGCO0VL5CU1pdPUrNBi9SzDbXTjzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:35:25.591148Z"},"content_sha256":"5f290a364cd4684afa4678e285d20af1368d2fb89d16cf53325621fe53108f65","schema_version":"1.0","event_id":"sha256:5f290a364cd4684afa4678e285d20af1368d2fb89d16cf53325621fe53108f65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QU3GL343XPM2LCTLIV6PHAD3OL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality Properties of Gaussian Quadrature, The Derivative Rule, and a Novel Approach to Stieltjes Inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.SP"],"primary_cat":"math.NA","authors_text":"William P. Reinhardt","submitted_at":"2018-12-05T19:25:27Z","abstract_excerpt":"Stieltjes, Perron, and Markov in analysis of the moment problem, for absolutely continuous measures, constructed the underlying measure as the discontinuity across the cut of a Cauchy representation of an otherwise real-analytic function. Introduction of Gaussian quadratures suggests more direct approaches. The real, positive, and continuous weight function, rho(x), is constructed directly from interpolation of the zeros, x[k], and weights, w[k], of the polynomials orthogonal for that measure. This novel numerical approach rests on a simple theorem: namely, rho(x[k]), evaluated at the quadratu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02196","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":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vl5ywOilRDfVc9e62dDuNCMfQWHJq4Wlok0HbP/XxtqE8b+kYERBwWpYQw0mMARCByGOHI3C/abmQpADTLLvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:35:25.591517Z"},"content_sha256":"fe79b1332ee0e5da9ad72ac57a3f15f5baea211ada84e75ad34aab9ce56cbece","schema_version":"1.0","event_id":"sha256:fe79b1332ee0e5da9ad72ac57a3f15f5baea211ada84e75ad34aab9ce56cbece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QU3GL343XPM2LCTLIV6PHAD3OL/bundle.json","state_url":"https://pith.science/pith/QU3GL343XPM2LCTLIV6PHAD3OL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QU3GL343XPM2LCTLIV6PHAD3OL/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":"2026-06-23T15:35:25Z","links":{"resolver":"https://pith.science/pith/QU3GL343XPM2LCTLIV6PHAD3OL","bundle":"https://pith.science/pith/QU3GL343XPM2LCTLIV6PHAD3OL/bundle.json","state":"https://pith.science/pith/QU3GL343XPM2LCTLIV6PHAD3OL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QU3GL343XPM2LCTLIV6PHAD3OL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QU3GL343XPM2LCTLIV6PHAD3OL","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":"a526ed4bca77ab4b5b9a817c151fe818f7c28830ce5c73f2bbe8de55c9a8dfce","cross_cats_sorted":["math-ph","math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-05T19:25:27Z","title_canon_sha256":"556a802a8f4d7a189f1ce8d434c3adafa3ce4ebcfce26476cba1d32efe3b2299"},"schema_version":"1.0","source":{"id":"1812.02196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02196","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02196v1","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02196","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"QU3GL343XPM2","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QU3GL343XPM2LCTL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QU3GL343","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:fe79b1332ee0e5da9ad72ac57a3f15f5baea211ada84e75ad34aab9ce56cbece","target":"graph","created_at":"2026-05-17T23:58:47Z","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":"Stieltjes, Perron, and Markov in analysis of the moment problem, for absolutely continuous measures, constructed the underlying measure as the discontinuity across the cut of a Cauchy representation of an otherwise real-analytic function. Introduction of Gaussian quadratures suggests more direct approaches. The real, positive, and continuous weight function, rho(x), is constructed directly from interpolation of the zeros, x[k], and weights, w[k], of the polynomials orthogonal for that measure. This novel numerical approach rests on a simple theorem: namely, rho(x[k]), evaluated at the quadratu","authors_text":"William P. Reinhardt","cross_cats":["math-ph","math.CA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-05T19:25:27Z","title":"Universality Properties of Gaussian Quadrature, The Derivative Rule, and a Novel Approach to Stieltjes Inversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02196","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":"sha256:5f290a364cd4684afa4678e285d20af1368d2fb89d16cf53325621fe53108f65","target":"record","created_at":"2026-05-17T23:58:47Z","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":"a526ed4bca77ab4b5b9a817c151fe818f7c28830ce5c73f2bbe8de55c9a8dfce","cross_cats_sorted":["math-ph","math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-05T19:25:27Z","title_canon_sha256":"556a802a8f4d7a189f1ce8d434c3adafa3ce4ebcfce26476cba1d32efe3b2299"},"schema_version":"1.0","source":{"id":"1812.02196","kind":"arxiv","version":1}},"canonical_sha256":"853665ef9bbbd9a58a6b457cf3807b72cf49fbeeea7225e58cb6ea8e8deaae46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"853665ef9bbbd9a58a6b457cf3807b72cf49fbeeea7225e58cb6ea8e8deaae46","first_computed_at":"2026-05-17T23:58:47.063628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:47.063628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJqVyI0YcDpjr5EwLtifzgCxSvd/RqVTWc+JvQTYYUGOtVv/jhQiLgZFWPJU0oC/UTNWANXaGnKjAyF1/Qt9Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:47.063985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f290a364cd4684afa4678e285d20af1368d2fb89d16cf53325621fe53108f65","sha256:fe79b1332ee0e5da9ad72ac57a3f15f5baea211ada84e75ad34aab9ce56cbece"],"state_sha256":"91c39850b9185e8cab27798eea68b05bc803e635c07f379c8fee30e4f2ddea98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5irQM7qKLj02ZHV0aABSaIg96YmtbhGT5Oj0rlFr25VkkWICpauzyyTloqV2Haxdf8pziY/DgjW8DfbrZdABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:35:25.593505Z","bundle_sha256":"f4348c9b7f96d653d5013616bf4917f8ed6e5c6631847f3590ae7ef9b7de7575"}}