{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CJDKNNXES3NY6PEYF26NSZX4R4","short_pith_number":"pith:CJDKNNXE","canonical_record":{"source":{"id":"1709.04562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-13T23:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"cfaa54e8ff0dd53604bcc73d4e274423f7c014abd7d6d04c4519c8977e64b0e4","abstract_canon_sha256":"d2e93eec350e461f20f93f052a1d85ca15ae7ceb2dab2bff6e71ae603558e257"},"schema_version":"1.0"},"canonical_sha256":"1246a6b6e496db8f3c982ebcd966fc8f37a42713d22cffbe5715db06efd9e493","source":{"kind":"arxiv","id":"1709.04562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04562","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04562v2","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04562","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"CJDKNNXES3NY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJDKNNXES3NY6PEY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJDKNNXE","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CJDKNNXES3NY6PEYF26NSZX4R4","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-13T23:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"cfaa54e8ff0dd53604bcc73d4e274423f7c014abd7d6d04c4519c8977e64b0e4","abstract_canon_sha256":"d2e93eec350e461f20f93f052a1d85ca15ae7ceb2dab2bff6e71ae603558e257"},"schema_version":"1.0"},"canonical_sha256":"1246a6b6e496db8f3c982ebcd966fc8f37a42713d22cffbe5715db06efd9e493","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:10.355767Z","signature_b64":"daxPWlYgxSnR0TsMOIEQG2ynTwzY4uFbM6ba0CSBQMEzKQ8Si5CoRXzxH2ZXVcQbydcWDh0A5tgFLMQ8ah5rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1246a6b6e496db8f3c982ebcd966fc8f37a42713d22cffbe5715db06efd9e493","last_reissued_at":"2026-05-18T00:29:10.355325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:10.355325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04562","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":"2026-05-18T00:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwqPsbcrk1IFkIt8m3fd6T80jGAl+uisZzbUbuKJppgkZK8IuUYnUzpXTx8LgvlPf9Szy4CBdz3YXpKRrDtKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:38:17.064336Z"},"content_sha256":"ba131647b6e1dff3fe77680d415271b9906adc677db622b506d28b478f79b450","schema_version":"1.0","event_id":"sha256:ba131647b6e1dff3fe77680d415271b9906adc677db622b506d28b478f79b450"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CJDKNNXES3NY6PEYF26NSZX4R4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient adaptive sparse grid collocation method through derivative estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anindya Bhaduri, Lori Graham-Brady","submitted_at":"2017-09-13T23:13:11Z","abstract_excerpt":"For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is of paramount importance. Sparse grid approaches have proven effective in reducing the number of sample evaluations. For example, the discrete projection collocation method has the notable feature of exhibiting fast convergence rates when approximating smooth functions; however, it lacks the ability to accurately and efficiently track response functions that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04562","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":"2026-05-18T00:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3RsllCQQxrsj50MZZsLtLvJh2HjeiQLnJFv6H/3GDTCC+7l2+jY8SXZ+RShSxNQqx2KDT0LVwi57Mida1kvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:38:17.064709Z"},"content_sha256":"08221580fa418b286c0f04bfcaa9f75f9c8144b9fc333079ac5a16916e842a11","schema_version":"1.0","event_id":"sha256:08221580fa418b286c0f04bfcaa9f75f9c8144b9fc333079ac5a16916e842a11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJDKNNXES3NY6PEYF26NSZX4R4/bundle.json","state_url":"https://pith.science/pith/CJDKNNXES3NY6PEYF26NSZX4R4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJDKNNXES3NY6PEYF26NSZX4R4/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":"2026-06-03T17:38:17Z","links":{"resolver":"https://pith.science/pith/CJDKNNXES3NY6PEYF26NSZX4R4","bundle":"https://pith.science/pith/CJDKNNXES3NY6PEYF26NSZX4R4/bundle.json","state":"https://pith.science/pith/CJDKNNXES3NY6PEYF26NSZX4R4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJDKNNXES3NY6PEYF26NSZX4R4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CJDKNNXES3NY6PEYF26NSZX4R4","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":"d2e93eec350e461f20f93f052a1d85ca15ae7ceb2dab2bff6e71ae603558e257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-13T23:13:11Z","title_canon_sha256":"cfaa54e8ff0dd53604bcc73d4e274423f7c014abd7d6d04c4519c8977e64b0e4"},"schema_version":"1.0","source":{"id":"1709.04562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04562","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04562v2","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04562","created_at":"2026-05-18T00:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"CJDKNNXES3NY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJDKNNXES3NY6PEY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJDKNNXE","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:08221580fa418b286c0f04bfcaa9f75f9c8144b9fc333079ac5a16916e842a11","target":"graph","created_at":"2026-05-18T00:29:10Z","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":"For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is of paramount importance. Sparse grid approaches have proven effective in reducing the number of sample evaluations. For example, the discrete projection collocation method has the notable feature of exhibiting fast convergence rates when approximating smooth functions; however, it lacks the ability to accurately and efficiently track response functions that","authors_text":"Anindya Bhaduri, Lori Graham-Brady","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-13T23:13:11Z","title":"An efficient adaptive sparse grid collocation method through derivative estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04562","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:ba131647b6e1dff3fe77680d415271b9906adc677db622b506d28b478f79b450","target":"record","created_at":"2026-05-18T00:29:10Z","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":"d2e93eec350e461f20f93f052a1d85ca15ae7ceb2dab2bff6e71ae603558e257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-13T23:13:11Z","title_canon_sha256":"cfaa54e8ff0dd53604bcc73d4e274423f7c014abd7d6d04c4519c8977e64b0e4"},"schema_version":"1.0","source":{"id":"1709.04562","kind":"arxiv","version":2}},"canonical_sha256":"1246a6b6e496db8f3c982ebcd966fc8f37a42713d22cffbe5715db06efd9e493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1246a6b6e496db8f3c982ebcd966fc8f37a42713d22cffbe5715db06efd9e493","first_computed_at":"2026-05-18T00:29:10.355325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:10.355325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"daxPWlYgxSnR0TsMOIEQG2ynTwzY4uFbM6ba0CSBQMEzKQ8Si5CoRXzxH2ZXVcQbydcWDh0A5tgFLMQ8ah5rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:10.355767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba131647b6e1dff3fe77680d415271b9906adc677db622b506d28b478f79b450","sha256:08221580fa418b286c0f04bfcaa9f75f9c8144b9fc333079ac5a16916e842a11"],"state_sha256":"0bd6abc2a9a1925fb43d36500be238ebbbb2b6c93ec519fd8a49583d4c2303a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YqDa0zfzEpAl13vYG0HyN11Bkw8BQmMSTj9axdB+v7WpXt08Cr7xmIb8oJ63bc6pCg2WfIXsw/tuVKxoEjlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:38:17.066664Z","bundle_sha256":"dbcd7fda451a8e71e21ae12ac610d48345874f70d64045175aa228e85dd30989"}}