{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:U6FHGRHIOBMQDQ5GYLNSUSAY53","short_pith_number":"pith:U6FHGRHI","canonical_record":{"source":{"id":"1403.6579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-26T07:17:39Z","cross_cats_sorted":[],"title_canon_sha256":"1b1db180848ed5345e053c78192c7729f3946376f14654fc34888b443735f653","abstract_canon_sha256":"c11d152c2a38f73f6d2786433dcd517a9117ae88cf46ba61950ec88242424cb0"},"schema_version":"1.0"},"canonical_sha256":"a78a7344e8705901c3a6c2db2a4818eec504b57f6bbc91b2e33cdd9df66e0f46","source":{"kind":"arxiv","id":"1403.6579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6579","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6579v1","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6579","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"U6FHGRHIOBMQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6FHGRHIOBMQDQ5G","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6FHGRHI","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:U6FHGRHIOBMQDQ5GYLNSUSAY53","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-26T07:17:39Z","cross_cats_sorted":[],"title_canon_sha256":"1b1db180848ed5345e053c78192c7729f3946376f14654fc34888b443735f653","abstract_canon_sha256":"c11d152c2a38f73f6d2786433dcd517a9117ae88cf46ba61950ec88242424cb0"},"schema_version":"1.0"},"canonical_sha256":"a78a7344e8705901c3a6c2db2a4818eec504b57f6bbc91b2e33cdd9df66e0f46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:28.599654Z","signature_b64":"1Njgr4DW/rxy3UZoE97VXR1/f65igy6ddGcQFDHeEO1c+Q/mNOr0uPl5ktuCJEwBtv27dc8f7MtqD86wc9KTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a78a7344e8705901c3a6c2db2a4818eec504b57f6bbc91b2e33cdd9df66e0f46","last_reissued_at":"2026-05-18T02:55:28.598961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:28.598961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6579","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":"2026-05-18T02:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zobIQEbZ0pyNVUmAwWL1BgYgYZcagfC3rYOB/YimlQtxhpGHP2JCTgf/F3O7O+K5POHylnDKllVMIYCGt4HiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:49:57.244498Z"},"content_sha256":"2500d751880be4506d82c49cfef79d43552b63df99b484d8f984fc83e30c578d","schema_version":"1.0","event_id":"sha256:2500d751880be4506d82c49cfef79d43552b63df99b484d8f984fc83e30c578d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:U6FHGRHIOBMQDQ5GYLNSUSAY53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On discrete least square projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Tao Tang, Tao Zhou","submitted_at":"2014-03-26T07:17:39Z","abstract_excerpt":"This work is concerned with approximating multivariate functions in unbounded domain by using discrete least-squares projection with random points evaluations. Particular attention are given to functions with random Gaussian or Gamma parameters. We first demonstrate that the traditional Hermite (Laguerre) polynomials chaos expansion suffers from the \\textit{instability} in the sense that an \\textit{unfeasible} number of points, which is relevant to the dimension of the approximation space, is needed to guarantee the stability in the least square framework. We then propose to use the Hermite/La"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6579","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":"2026-05-18T02:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OZKcBTlopWjIStI5aMlT+8uB+mDmCNGP8RH/ojgsFgUQiXFsQ69Re6J7KiLLfvXDqicvqKt77vYrip7RwyrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:49:57.245258Z"},"content_sha256":"89ab8c9acc04ffb0c33a31b4d316a07ed78e391dbf857fa6d108526c8aff84ab","schema_version":"1.0","event_id":"sha256:89ab8c9acc04ffb0c33a31b4d316a07ed78e391dbf857fa6d108526c8aff84ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/bundle.json","state_url":"https://pith.science/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/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":"2026-06-10T05:49:57Z","links":{"resolver":"https://pith.science/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53","bundle":"https://pith.science/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/bundle.json","state":"https://pith.science/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6FHGRHIOBMQDQ5GYLNSUSAY53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:U6FHGRHIOBMQDQ5GYLNSUSAY53","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":"c11d152c2a38f73f6d2786433dcd517a9117ae88cf46ba61950ec88242424cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-26T07:17:39Z","title_canon_sha256":"1b1db180848ed5345e053c78192c7729f3946376f14654fc34888b443735f653"},"schema_version":"1.0","source":{"id":"1403.6579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6579","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6579v1","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6579","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"U6FHGRHIOBMQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6FHGRHIOBMQDQ5G","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6FHGRHI","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:89ab8c9acc04ffb0c33a31b4d316a07ed78e391dbf857fa6d108526c8aff84ab","target":"graph","created_at":"2026-05-18T02:55:28Z","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":"This work is concerned with approximating multivariate functions in unbounded domain by using discrete least-squares projection with random points evaluations. Particular attention are given to functions with random Gaussian or Gamma parameters. We first demonstrate that the traditional Hermite (Laguerre) polynomials chaos expansion suffers from the \\textit{instability} in the sense that an \\textit{unfeasible} number of points, which is relevant to the dimension of the approximation space, is needed to guarantee the stability in the least square framework. We then propose to use the Hermite/La","authors_text":"Tao Tang, Tao Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-26T07:17:39Z","title":"On discrete least square projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6579","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":"sha256:2500d751880be4506d82c49cfef79d43552b63df99b484d8f984fc83e30c578d","target":"record","created_at":"2026-05-18T02:55:28Z","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":"c11d152c2a38f73f6d2786433dcd517a9117ae88cf46ba61950ec88242424cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-26T07:17:39Z","title_canon_sha256":"1b1db180848ed5345e053c78192c7729f3946376f14654fc34888b443735f653"},"schema_version":"1.0","source":{"id":"1403.6579","kind":"arxiv","version":1}},"canonical_sha256":"a78a7344e8705901c3a6c2db2a4818eec504b57f6bbc91b2e33cdd9df66e0f46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a78a7344e8705901c3a6c2db2a4818eec504b57f6bbc91b2e33cdd9df66e0f46","first_computed_at":"2026-05-18T02:55:28.598961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:28.598961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Njgr4DW/rxy3UZoE97VXR1/f65igy6ddGcQFDHeEO1c+Q/mNOr0uPl5ktuCJEwBtv27dc8f7MtqD86wc9KTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:28.599654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2500d751880be4506d82c49cfef79d43552b63df99b484d8f984fc83e30c578d","sha256:89ab8c9acc04ffb0c33a31b4d316a07ed78e391dbf857fa6d108526c8aff84ab"],"state_sha256":"cf6a87d7eb5ffdb5f4d64605fefc32b04dff03b1f0bb72cd304df107d756b703"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/Tr/l5mRlBq8dL0FNEYsDUcYuoP1iophAWP+Evnh0SG90M5SvkkHSjk6CtcOBAiiWS6H8ubn1kkwDM/wgaPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:49:57.249598Z","bundle_sha256":"c37d6433899f374cb91e8370d4e80fea0c99890d9f87aec319e7ac1124457ff5"}}