{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MQYMSTTBC3JWUPZSNBAKZDRRX3","short_pith_number":"pith:MQYMSTTB","canonical_record":{"source":{"id":"1904.02017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T14:18:04Z","cross_cats_sorted":[],"title_canon_sha256":"c846e2ce147a2cc2174ef2e8e665015670cfbe85cf8d38a5f5cbedc5a340fd33","abstract_canon_sha256":"2c83e0f11a7aa2d7e120e401919b79468a4c8cf16b7309d4c63733ec58223a93"},"schema_version":"1.0"},"canonical_sha256":"6430c94e6116d36a3f326840ac8e31bef4eec1ac2b912def29886adcb7e7ce90","source":{"kind":"arxiv","id":"1904.02017","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02017","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02017v2","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02017","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"MQYMSTTBC3JW","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MQYMSTTBC3JWUPZS","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MQYMSTTB","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MQYMSTTBC3JWUPZSNBAKZDRRX3","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T14:18:04Z","cross_cats_sorted":[],"title_canon_sha256":"c846e2ce147a2cc2174ef2e8e665015670cfbe85cf8d38a5f5cbedc5a340fd33","abstract_canon_sha256":"2c83e0f11a7aa2d7e120e401919b79468a4c8cf16b7309d4c63733ec58223a93"},"schema_version":"1.0"},"canonical_sha256":"6430c94e6116d36a3f326840ac8e31bef4eec1ac2b912def29886adcb7e7ce90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:20.030889Z","signature_b64":"J7Emr7OsreNYlcSSLR04q+ayssrUINxMKPbESGDb3U913eoN3igquwcTRoRI2CCLXizaQASh7Qq2Uh31YJlWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6430c94e6116d36a3f326840ac8e31bef4eec1ac2b912def29886adcb7e7ce90","last_reissued_at":"2026-05-17T23:49:20.029649Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:20.029649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02017","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":"2026-05-17T23:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCLexDMp/1SasMEA7iVdG7zoWQMEIMjKczjJlDQrIwbmZ2+d+Sw1JMjKd11NXAzbzONarPkfPcG2bI1x03mjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:15:42.314673Z"},"content_sha256":"e4ed9ec704b7ac4a447f507ee7d6945dc58f5ced9b73410bc156635940c0d3af","schema_version":"1.0","event_id":"sha256:e4ed9ec704b7ac4a447f507ee7d6945dc58f5ced9b73410bc156635940c0d3af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MQYMSTTBC3JWUPZSNBAKZDRRX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poly-Sinc Solution of Stochastic Elliptic Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Maha Youssef, Roland Pulch","submitted_at":"2019-04-03T14:18:04Z","abstract_excerpt":"In this paper, we introduce a numerical solution of a stochastic partial differential equation (SPDE) of elliptic type using polynomial chaos along side with polynomial approximation at Sinc points. These Sinc points are defined by a conformal map and when mixed with the polynomial interpolation, it yields an accurate approximation. The first step to solve SPDE is to use stochastic Galerkin method in conjunction with polynomial chaos, which implies a system of deterministic partial differential equations to be solved. The main difficulty is the higher dimensionality of the resulting system of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02017","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":"2026-05-17T23:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYUQ3aKKrVVSiI91fyLbfn+73FMAyNtfYMwOxWO15KMCDlpQBoJqDEOwqTdb7JjXuaemPGsbortxyVul5f3VAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:15:42.315294Z"},"content_sha256":"6666d6c6e6a5a18a9d6b03ca521be7ff33748cfc382cb55890a3b381c1d44a0d","schema_version":"1.0","event_id":"sha256:6666d6c6e6a5a18a9d6b03ca521be7ff33748cfc382cb55890a3b381c1d44a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/bundle.json","state_url":"https://pith.science/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/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":"2026-06-08T14:15:42Z","links":{"resolver":"https://pith.science/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3","bundle":"https://pith.science/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/bundle.json","state":"https://pith.science/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQYMSTTBC3JWUPZSNBAKZDRRX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MQYMSTTBC3JWUPZSNBAKZDRRX3","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":"2c83e0f11a7aa2d7e120e401919b79468a4c8cf16b7309d4c63733ec58223a93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T14:18:04Z","title_canon_sha256":"c846e2ce147a2cc2174ef2e8e665015670cfbe85cf8d38a5f5cbedc5a340fd33"},"schema_version":"1.0","source":{"id":"1904.02017","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02017","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02017v2","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02017","created_at":"2026-05-17T23:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"MQYMSTTBC3JW","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MQYMSTTBC3JWUPZS","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MQYMSTTB","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:6666d6c6e6a5a18a9d6b03ca521be7ff33748cfc382cb55890a3b381c1d44a0d","target":"graph","created_at":"2026-05-17T23:49:20Z","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 this paper, we introduce a numerical solution of a stochastic partial differential equation (SPDE) of elliptic type using polynomial chaos along side with polynomial approximation at Sinc points. These Sinc points are defined by a conformal map and when mixed with the polynomial interpolation, it yields an accurate approximation. The first step to solve SPDE is to use stochastic Galerkin method in conjunction with polynomial chaos, which implies a system of deterministic partial differential equations to be solved. The main difficulty is the higher dimensionality of the resulting system of ","authors_text":"Maha Youssef, Roland Pulch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T14:18:04Z","title":"Poly-Sinc Solution of Stochastic Elliptic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02017","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:e4ed9ec704b7ac4a447f507ee7d6945dc58f5ced9b73410bc156635940c0d3af","target":"record","created_at":"2026-05-17T23:49:20Z","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":"2c83e0f11a7aa2d7e120e401919b79468a4c8cf16b7309d4c63733ec58223a93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T14:18:04Z","title_canon_sha256":"c846e2ce147a2cc2174ef2e8e665015670cfbe85cf8d38a5f5cbedc5a340fd33"},"schema_version":"1.0","source":{"id":"1904.02017","kind":"arxiv","version":2}},"canonical_sha256":"6430c94e6116d36a3f326840ac8e31bef4eec1ac2b912def29886adcb7e7ce90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6430c94e6116d36a3f326840ac8e31bef4eec1ac2b912def29886adcb7e7ce90","first_computed_at":"2026-05-17T23:49:20.029649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:20.029649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7Emr7OsreNYlcSSLR04q+ayssrUINxMKPbESGDb3U913eoN3igquwcTRoRI2CCLXizaQASh7Qq2Uh31YJlWBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:20.030889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02017","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4ed9ec704b7ac4a447f507ee7d6945dc58f5ced9b73410bc156635940c0d3af","sha256:6666d6c6e6a5a18a9d6b03ca521be7ff33748cfc382cb55890a3b381c1d44a0d"],"state_sha256":"cc7a58abd27f6b1943f5aa8f0a5799f7b88048a71b25b5c97ce6d4aa40db5265"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1x1VOHyvVPafCaeeHkO0UeFZTJdV1pz6TWAdBkGO3IzCDVjWs7YNa0e8gPPfdMyPmvs4IcmZfm0bmDtvpwpaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:15:42.318646Z","bundle_sha256":"8e2a95d97aec432a586145de422a0f39ea5431a53c3ad8929d966ab260e4bb6e"}}