{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JPHYU7LUQDUJKE7MEZNUXUM7KM","short_pith_number":"pith:JPHYU7LU","canonical_record":{"source":{"id":"1409.4829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T23:15:01Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"3ed63d0d922bae4379712e40af88de1e547d09b215906d84c1a7f2c7441c8f65","abstract_canon_sha256":"464fb39414e01fb236253eb749a2a6fe70ab6fa1747c90ab38c270ea8ffe58cd"},"schema_version":"1.0"},"canonical_sha256":"4bcf8a7d7480e89513ec265b4bd19f53398e9773f19c58a3a2f1c336214a3444","source":{"kind":"arxiv","id":"1409.4829","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4829","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4829v1","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4829","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"JPHYU7LUQDUJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JPHYU7LUQDUJKE7M","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JPHYU7LU","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JPHYU7LUQDUJKE7MEZNUXUM7KM","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T23:15:01Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"3ed63d0d922bae4379712e40af88de1e547d09b215906d84c1a7f2c7441c8f65","abstract_canon_sha256":"464fb39414e01fb236253eb749a2a6fe70ab6fa1747c90ab38c270ea8ffe58cd"},"schema_version":"1.0"},"canonical_sha256":"4bcf8a7d7480e89513ec265b4bd19f53398e9773f19c58a3a2f1c336214a3444","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:51.516536Z","signature_b64":"d3QE7U+6swdxMx2iOa7oMnwgKlvTLyRw+exIUh1SCzUbZBAT0xdGzJKhNQ+Wcnrvn0LiiC4o8Qf4UKWEJFcEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bcf8a7d7480e89513ec265b4bd19f53398e9773f19c58a3a2f1c336214a3444","last_reissued_at":"2026-05-18T00:57:51.516066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:51.516066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4829","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":"2026-05-18T00:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FmIIzkOd1Ido7Ty0g+d/Wg+H+eZMJPzfDmH4IpKYDOLFtOhHDUdmseLjv6f2KYTQpZqldTDZyNT9nianr0x0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:33:08.299546Z"},"content_sha256":"7dbc04e9e4c285b74a9dbdf7768cff76dfc6d7835f1ad26e119326c9e369cef4","schema_version":"1.0","event_id":"sha256:7dbc04e9e4c285b74a9dbdf7768cff76dfc6d7835f1ad26e119326c9e369cef4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JPHYU7LUQDUJKE7MEZNUXUM7KM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.CE","authors_text":"Ibrahim (Abe) M. Elfadel, Luca Daniel, Tarek A. El-Moselhy, Zheng Zhang","submitted_at":"2014-09-16T23:15:01Z","abstract_excerpt":"Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\\it a-priori}. However, indiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4829","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":"2026-05-18T00:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7miv7zWIWTxz4TYnxMPbfDvDJPP0l6dXQTquKcvGWJaIxOLs2/d6KOPQYMWXqD+XwcZrMHYxtcdGDo4VeXGbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:33:08.299892Z"},"content_sha256":"d9f1dd5a916377fd263e8d69f26c4998501bfee7d0be015fbaf85212c93cbb8b","schema_version":"1.0","event_id":"sha256:d9f1dd5a916377fd263e8d69f26c4998501bfee7d0be015fbaf85212c93cbb8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/bundle.json","state_url":"https://pith.science/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/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":"2026-06-21T05:33:08Z","links":{"resolver":"https://pith.science/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM","bundle":"https://pith.science/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/bundle.json","state":"https://pith.science/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPHYU7LUQDUJKE7MEZNUXUM7KM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JPHYU7LUQDUJKE7MEZNUXUM7KM","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":"464fb39414e01fb236253eb749a2a6fe70ab6fa1747c90ab38c270ea8ffe58cd","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T23:15:01Z","title_canon_sha256":"3ed63d0d922bae4379712e40af88de1e547d09b215906d84c1a7f2c7441c8f65"},"schema_version":"1.0","source":{"id":"1409.4829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4829","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4829v1","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4829","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"JPHYU7LUQDUJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JPHYU7LUQDUJKE7M","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JPHYU7LU","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d9f1dd5a916377fd263e8d69f26c4998501bfee7d0be015fbaf85212c93cbb8b","target":"graph","created_at":"2026-05-18T00:57:51Z","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":"Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\\it a-priori}. However, indiv","authors_text":"Ibrahim (Abe) M. Elfadel, Luca Daniel, Tarek A. El-Moselhy, Zheng Zhang","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T23:15:01Z","title":"Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4829","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":"sha256:7dbc04e9e4c285b74a9dbdf7768cff76dfc6d7835f1ad26e119326c9e369cef4","target":"record","created_at":"2026-05-18T00:57:51Z","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":"464fb39414e01fb236253eb749a2a6fe70ab6fa1747c90ab38c270ea8ffe58cd","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T23:15:01Z","title_canon_sha256":"3ed63d0d922bae4379712e40af88de1e547d09b215906d84c1a7f2c7441c8f65"},"schema_version":"1.0","source":{"id":"1409.4829","kind":"arxiv","version":1}},"canonical_sha256":"4bcf8a7d7480e89513ec265b4bd19f53398e9773f19c58a3a2f1c336214a3444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bcf8a7d7480e89513ec265b4bd19f53398e9773f19c58a3a2f1c336214a3444","first_computed_at":"2026-05-18T00:57:51.516066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:51.516066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d3QE7U+6swdxMx2iOa7oMnwgKlvTLyRw+exIUh1SCzUbZBAT0xdGzJKhNQ+Wcnrvn0LiiC4o8Qf4UKWEJFcEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:51.516536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dbc04e9e4c285b74a9dbdf7768cff76dfc6d7835f1ad26e119326c9e369cef4","sha256:d9f1dd5a916377fd263e8d69f26c4998501bfee7d0be015fbaf85212c93cbb8b"],"state_sha256":"ad23e3908b4c7a9f279cfb7b0b0e1079308f1a386991688100b39b97caf055a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jq31A1LOXPPCeqHhxAO09yhhKO/7fSNUuV7o/MVOMPc6QjgWHskx68tEP2pgXnBh2ZmRivVm4EuuWkKn4rc7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T05:33:08.301780Z","bundle_sha256":"8cd3479c3b515a7a2633d4c2b3731c795f220714392c1b8c47cb050bcc7d5602"}}