{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JS2NNFXX5LTTAGOYZWQYVKW6PG","short_pith_number":"pith:JS2NNFXX","canonical_record":{"source":{"id":"1511.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-23T22:21:42Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"4e66380981a6bd0b24cd3a1f18c49bab16eeb7a3dd8042958556b95582855f9c","abstract_canon_sha256":"0404fcdc3a5fac278aaf48ab2570d6bc95094dafa7737adfbb4b2d729bf67b83"},"schema_version":"1.0"},"canonical_sha256":"4cb4d696f7eae73019d8cda18aaade79ab472219d4cdcda8bb17f7987eeb0bc4","source":{"kind":"arxiv","id":"1511.07492","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07492","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07492v2","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07492","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"JS2NNFXX5LTT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JS2NNFXX5LTTAGOY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JS2NNFXX","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JS2NNFXX5LTTAGOYZWQYVKW6PG","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-23T22:21:42Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"4e66380981a6bd0b24cd3a1f18c49bab16eeb7a3dd8042958556b95582855f9c","abstract_canon_sha256":"0404fcdc3a5fac278aaf48ab2570d6bc95094dafa7737adfbb4b2d729bf67b83"},"schema_version":"1.0"},"canonical_sha256":"4cb4d696f7eae73019d8cda18aaade79ab472219d4cdcda8bb17f7987eeb0bc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:19.015624Z","signature_b64":"R2JPuMH0Qtv7/Z4KOKktdbkC6eeOxQ4y1z3nLHigkR9jd08OE8Q5pJ6NlG/RWDwra/7pEmTgCq7xALgmXDhyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cb4d696f7eae73019d8cda18aaade79ab472219d4cdcda8bb17f7987eeb0bc4","last_reissued_at":"2026-05-18T01:08:19.015102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:19.015102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07492","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":"2026-05-18T01:08:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdbk6WqAwAlVIbeTYdWv01SD3DVW8K7TKgOY6vwZIySSK5VfJp8YrQebrjXD5aq2lKeohR2yZOOvcecqgc32Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:05:57.944267Z"},"content_sha256":"f874e863dd8c8c73c1927d93a92946fef6112bc0f72ff77bcc5e19380b056cd1","schema_version":"1.0","event_id":"sha256:f874e863dd8c8c73c1927d93a92946fef6112bc0f72ff77bcc5e19380b056cd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JS2NNFXX5LTTAGOYZWQYVKW6PG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial meta-models with canonical low-rank approximations: numerical insights and comparison to sparse polynomial chaos expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Bruno Sudret, Katerina Konakli","submitted_at":"2015-11-23T22:21:42Z","abstract_excerpt":"The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07492","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":"2026-05-18T01:08:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2zpy4tSd7DARxLmeJExuO1cpT6yu2x/f3a2+qcE4s7yjALMQFq9BxLHxRyg7XsFapk916CkddKtikWHSMDNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:05:57.945049Z"},"content_sha256":"b34cd54db1ead1adfa55b0340e915f989dfe2047d51ac405ec7f12c5232278e9","schema_version":"1.0","event_id":"sha256:b34cd54db1ead1adfa55b0340e915f989dfe2047d51ac405ec7f12c5232278e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/bundle.json","state_url":"https://pith.science/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/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":"2026-05-31T11:05:57Z","links":{"resolver":"https://pith.science/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG","bundle":"https://pith.science/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/bundle.json","state":"https://pith.science/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JS2NNFXX5LTTAGOYZWQYVKW6PG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JS2NNFXX5LTTAGOYZWQYVKW6PG","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":"0404fcdc3a5fac278aaf48ab2570d6bc95094dafa7737adfbb4b2d729bf67b83","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-23T22:21:42Z","title_canon_sha256":"4e66380981a6bd0b24cd3a1f18c49bab16eeb7a3dd8042958556b95582855f9c"},"schema_version":"1.0","source":{"id":"1511.07492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07492","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07492v2","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07492","created_at":"2026-05-18T01:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"JS2NNFXX5LTT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JS2NNFXX5LTTAGOY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JS2NNFXX","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:b34cd54db1ead1adfa55b0340e915f989dfe2047d51ac405ec7f12c5232278e9","target":"graph","created_at":"2026-05-18T01:08:19Z","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":"The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropria","authors_text":"Bruno Sudret, Katerina Konakli","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-23T22:21:42Z","title":"Polynomial meta-models with canonical low-rank approximations: numerical insights and comparison to sparse polynomial chaos expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07492","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:f874e863dd8c8c73c1927d93a92946fef6112bc0f72ff77bcc5e19380b056cd1","target":"record","created_at":"2026-05-18T01:08:19Z","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":"0404fcdc3a5fac278aaf48ab2570d6bc95094dafa7737adfbb4b2d729bf67b83","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-23T22:21:42Z","title_canon_sha256":"4e66380981a6bd0b24cd3a1f18c49bab16eeb7a3dd8042958556b95582855f9c"},"schema_version":"1.0","source":{"id":"1511.07492","kind":"arxiv","version":2}},"canonical_sha256":"4cb4d696f7eae73019d8cda18aaade79ab472219d4cdcda8bb17f7987eeb0bc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cb4d696f7eae73019d8cda18aaade79ab472219d4cdcda8bb17f7987eeb0bc4","first_computed_at":"2026-05-18T01:08:19.015102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:19.015102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R2JPuMH0Qtv7/Z4KOKktdbkC6eeOxQ4y1z3nLHigkR9jd08OE8Q5pJ6NlG/RWDwra/7pEmTgCq7xALgmXDhyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:19.015624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f874e863dd8c8c73c1927d93a92946fef6112bc0f72ff77bcc5e19380b056cd1","sha256:b34cd54db1ead1adfa55b0340e915f989dfe2047d51ac405ec7f12c5232278e9"],"state_sha256":"008ece701e9d1951238ad8116b9306843288f55b8733113dc0cfe7af61b28fb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9B0dZakSR+xvPxRy7QY6WYa6WvCnH+y2DGHjBSGSZaeefC58ZbjeVFuhetbO1f3HeaJG9DGjJB6ZSa9ljapkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:05:57.948963Z","bundle_sha256":"7fb2d3a8f18dbc0fe89b03d58b86f30fac1b2b438c08c13fafc5abf616ebd718"}}