{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LWAYKNEG5IECMFE73KP6YEX7WS","short_pith_number":"pith:LWAYKNEG","canonical_record":{"source":{"id":"1710.09254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-25T14:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"bd8a2facdd96a8f5d9ea75041e6a1f0bba48fbfc3508b3636761ed75a4aec005","abstract_canon_sha256":"87aaf288f0ac7832a5b99f246be612bad331cebfb03d2995bc1de5923102961f"},"schema_version":"1.0"},"canonical_sha256":"5d81853486ea0826149fda9fec12ffb49feb99acbf6c81f67ba40d4150653d25","source":{"kind":"arxiv","id":"1710.09254","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09254","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09254v2","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09254","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"LWAYKNEG5IEC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LWAYKNEG5IECMFE7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LWAYKNEG","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LWAYKNEG5IECMFE73KP6YEX7WS","target":"record","payload":{"canonical_record":{"source":{"id":"1710.09254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-25T14:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"bd8a2facdd96a8f5d9ea75041e6a1f0bba48fbfc3508b3636761ed75a4aec005","abstract_canon_sha256":"87aaf288f0ac7832a5b99f246be612bad331cebfb03d2995bc1de5923102961f"},"schema_version":"1.0"},"canonical_sha256":"5d81853486ea0826149fda9fec12ffb49feb99acbf6c81f67ba40d4150653d25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:41.662774Z","signature_b64":"qWyABeFog8EA+1jYFAAz9qGoN/9D47df639UqEN0c2qjcUgEczqzOPq/j90mMJv/9YcM9h0f4yj8VrBkXBsFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d81853486ea0826149fda9fec12ffb49feb99acbf6c81f67ba40d4150653d25","last_reissued_at":"2026-05-18T00:19:41.661972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:41.661972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.09254","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":"2026-05-18T00:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmOH1VLaT2dJnHDRSyk8WMums4N616+N6N2ieKLHKiRvQ/sfFDAsV2zfh/WqzcYu24xxDN+TvX9OWz4EhlspBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:50:53.014687Z"},"content_sha256":"6eb187dd97efcbfe9344664c98e7dbd60690a34a664b502425d2758ed36ecb00","schema_version":"1.0","event_id":"sha256:6eb187dd97efcbfe9344664c98e7dbd60690a34a664b502425d2758ed36ecb00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LWAYKNEG5IECMFE73KP6YEX7WS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dirk Nuyens, Frances Y. Kuo, Ian H. Sloan, Ivan G. Graham, Rob Scheichl","submitted_at":"2017-10-25T14:26:43Z","abstract_excerpt":"In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. This method was based on combining quasi-Monte Carlo (QMC) methods for computing the expected values with circulant embedding methods for sampling the random field on a regular grid. It was found capable of handling fluid flow problems in random heterogeneous media with high stochastic dimension, but a convergence theory was missing. This paper p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09254","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":"2026-05-18T00:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRzlB1GSBIRfBFB8cp9oFrN7PCJccgu4ftyTH2zaUGW6zNuaCdt64+oZiB4B9wvKv6rclL6ed+fok1cFzX92Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:50:53.015029Z"},"content_sha256":"1096ac1ef3fe3bf8d84760273f8c199b4fed276fca54fe95ec563fee96aec07b","schema_version":"1.0","event_id":"sha256:1096ac1ef3fe3bf8d84760273f8c199b4fed276fca54fe95ec563fee96aec07b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LWAYKNEG5IECMFE73KP6YEX7WS/bundle.json","state_url":"https://pith.science/pith/LWAYKNEG5IECMFE73KP6YEX7WS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LWAYKNEG5IECMFE73KP6YEX7WS/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":"2026-06-20T03:50:53Z","links":{"resolver":"https://pith.science/pith/LWAYKNEG5IECMFE73KP6YEX7WS","bundle":"https://pith.science/pith/LWAYKNEG5IECMFE73KP6YEX7WS/bundle.json","state":"https://pith.science/pith/LWAYKNEG5IECMFE73KP6YEX7WS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LWAYKNEG5IECMFE73KP6YEX7WS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LWAYKNEG5IECMFE73KP6YEX7WS","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":"87aaf288f0ac7832a5b99f246be612bad331cebfb03d2995bc1de5923102961f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-25T14:26:43Z","title_canon_sha256":"bd8a2facdd96a8f5d9ea75041e6a1f0bba48fbfc3508b3636761ed75a4aec005"},"schema_version":"1.0","source":{"id":"1710.09254","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09254","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09254v2","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09254","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"LWAYKNEG5IEC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LWAYKNEG5IECMFE7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LWAYKNEG","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:1096ac1ef3fe3bf8d84760273f8c199b4fed276fca54fe95ec563fee96aec07b","target":"graph","created_at":"2026-05-18T00:19:41Z","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":"In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. This method was based on combining quasi-Monte Carlo (QMC) methods for computing the expected values with circulant embedding methods for sampling the random field on a regular grid. It was found capable of handling fluid flow problems in random heterogeneous media with high stochastic dimension, but a convergence theory was missing. This paper p","authors_text":"Dirk Nuyens, Frances Y. Kuo, Ian H. Sloan, Ivan G. Graham, Rob Scheichl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-25T14:26:43Z","title":"Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09254","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":"sha256:6eb187dd97efcbfe9344664c98e7dbd60690a34a664b502425d2758ed36ecb00","target":"record","created_at":"2026-05-18T00:19:41Z","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":"87aaf288f0ac7832a5b99f246be612bad331cebfb03d2995bc1de5923102961f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-25T14:26:43Z","title_canon_sha256":"bd8a2facdd96a8f5d9ea75041e6a1f0bba48fbfc3508b3636761ed75a4aec005"},"schema_version":"1.0","source":{"id":"1710.09254","kind":"arxiv","version":2}},"canonical_sha256":"5d81853486ea0826149fda9fec12ffb49feb99acbf6c81f67ba40d4150653d25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d81853486ea0826149fda9fec12ffb49feb99acbf6c81f67ba40d4150653d25","first_computed_at":"2026-05-18T00:19:41.661972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:41.661972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qWyABeFog8EA+1jYFAAz9qGoN/9D47df639UqEN0c2qjcUgEczqzOPq/j90mMJv/9YcM9h0f4yj8VrBkXBsFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:41.662774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09254","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eb187dd97efcbfe9344664c98e7dbd60690a34a664b502425d2758ed36ecb00","sha256:1096ac1ef3fe3bf8d84760273f8c199b4fed276fca54fe95ec563fee96aec07b"],"state_sha256":"e031d38c16eda673798ffc48b987788d5e884e113b9a9e59179ff2bbf7e74a86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AlqkozFxTyhIoN2+GFU1aRzjF/EbaM5Et13aLkggrFL+57J7FQ/wthXjGHedUYFyqhpsj6p8seCs/iSFoUWACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:50:53.019785Z","bundle_sha256":"27fec7dc2da72cfe7c899af512069fe3a9f5223194d745eab94156de9c96c627"}}