{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TCRRXKLVI64KJVS2U5N4PPWQPB","short_pith_number":"pith:TCRRXKLV","canonical_record":{"source":{"id":"1809.06195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-17T13:35:00Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"a7b7a55fe74900d0da92829bc71525f7ad7e673b8eb6b1609f2e2420d3378e18","abstract_canon_sha256":"eda1a6c1155541c5c7966f523230a475afbc5c04b2a56d56d2ee34172a6b0d25"},"schema_version":"1.0"},"canonical_sha256":"98a31ba97547b8a4d65aa75bc7bed0784b159ce8be08303ed041c684fc66954a","source":{"kind":"arxiv","id":"1809.06195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06195","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06195v2","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06195","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"TCRRXKLVI64K","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TCRRXKLVI64KJVS2","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TCRRXKLV","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TCRRXKLVI64KJVS2U5N4PPWQPB","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-17T13:35:00Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"a7b7a55fe74900d0da92829bc71525f7ad7e673b8eb6b1609f2e2420d3378e18","abstract_canon_sha256":"eda1a6c1155541c5c7966f523230a475afbc5c04b2a56d56d2ee34172a6b0d25"},"schema_version":"1.0"},"canonical_sha256":"98a31ba97547b8a4d65aa75bc7bed0784b159ce8be08303ed041c684fc66954a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:49.112134Z","signature_b64":"W2ZJZhRWh787H+LSwSYBgwAuYEB46wneqQ2mFxnafjjr8LBfrUSzLeTP8ZQ5J3pHxTy90Yp/YP78F9idbQScBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98a31ba97547b8a4d65aa75bc7bed0784b159ce8be08303ed041c684fc66954a","last_reissued_at":"2026-05-17T23:51:49.111519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:49.111519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06195","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":"2026-05-17T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nEosOQvhK5QbcazL6+GEg+QR7VS5JvIMcaCuv+QViahqNZOEyPwqeFlWjwLTp6fCdHv4/iq4Ns+pS5IkNhOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:40.899126Z"},"content_sha256":"b6fb13a2b7998de4cef7543a16fc8dbd128ede5c58d83bc401b7005e6613da33","schema_version":"1.0","event_id":"sha256:b6fb13a2b7998de4cef7543a16fc8dbd128ede5c58d83bc401b7005e6613da33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TCRRXKLVI64KJVS2U5N4PPWQPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"math.NA","authors_text":"Roland Pulch, Sebastian Sch\\\"ops","submitted_at":"2018-09-17T13:35:00Z","abstract_excerpt":"We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters into random variables. A random quantity of interest is expanded into the (generalised) polynomial chaos using orthogonal basis polynomials. We investigate the determination of sparse representations, where just a few basis polynomials are required for a sufficiently accurate approximation. Furthermore, we apply model order reduction with p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06195","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":"2026-05-17T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zL/HPTQKpIpRDlYN9fxSx5PHgaC4As5na9QD9cG7QAXFBr2UgCEOhBgh+8EQqyWq8mkw6kyfsFw+2wBfNXJnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:40.899499Z"},"content_sha256":"105823aec600b298050460d77c957bc6804d41947a69f47c0773d66e52c1ae85","schema_version":"1.0","event_id":"sha256:105823aec600b298050460d77c957bc6804d41947a69f47c0773d66e52c1ae85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/bundle.json","state_url":"https://pith.science/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/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":"2026-06-04T04:22:40Z","links":{"resolver":"https://pith.science/pith/TCRRXKLVI64KJVS2U5N4PPWQPB","bundle":"https://pith.science/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/bundle.json","state":"https://pith.science/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCRRXKLVI64KJVS2U5N4PPWQPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TCRRXKLVI64KJVS2U5N4PPWQPB","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":"eda1a6c1155541c5c7966f523230a475afbc5c04b2a56d56d2ee34172a6b0d25","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-17T13:35:00Z","title_canon_sha256":"a7b7a55fe74900d0da92829bc71525f7ad7e673b8eb6b1609f2e2420d3378e18"},"schema_version":"1.0","source":{"id":"1809.06195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06195","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06195v2","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06195","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"TCRRXKLVI64K","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TCRRXKLVI64KJVS2","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TCRRXKLV","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:105823aec600b298050460d77c957bc6804d41947a69f47c0773d66e52c1ae85","target":"graph","created_at":"2026-05-17T23:51:49Z","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":"We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters into random variables. A random quantity of interest is expanded into the (generalised) polynomial chaos using orthogonal basis polynomials. We investigate the determination of sparse representations, where just a few basis polynomials are required for a sufficiently accurate approximation. Furthermore, we apply model order reduction with p","authors_text":"Roland Pulch, Sebastian Sch\\\"ops","cross_cats":["cs.CE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-17T13:35:00Z","title":"Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06195","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:b6fb13a2b7998de4cef7543a16fc8dbd128ede5c58d83bc401b7005e6613da33","target":"record","created_at":"2026-05-17T23:51:49Z","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":"eda1a6c1155541c5c7966f523230a475afbc5c04b2a56d56d2ee34172a6b0d25","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-17T13:35:00Z","title_canon_sha256":"a7b7a55fe74900d0da92829bc71525f7ad7e673b8eb6b1609f2e2420d3378e18"},"schema_version":"1.0","source":{"id":"1809.06195","kind":"arxiv","version":2}},"canonical_sha256":"98a31ba97547b8a4d65aa75bc7bed0784b159ce8be08303ed041c684fc66954a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98a31ba97547b8a4d65aa75bc7bed0784b159ce8be08303ed041c684fc66954a","first_computed_at":"2026-05-17T23:51:49.111519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:49.111519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2ZJZhRWh787H+LSwSYBgwAuYEB46wneqQ2mFxnafjjr8LBfrUSzLeTP8ZQ5J3pHxTy90Yp/YP78F9idbQScBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:49.112134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6fb13a2b7998de4cef7543a16fc8dbd128ede5c58d83bc401b7005e6613da33","sha256:105823aec600b298050460d77c957bc6804d41947a69f47c0773d66e52c1ae85"],"state_sha256":"c1951dd4f2589a7782f3cb11ae8d26d8177900650951aef8b4bc448838cd4f62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpKM78nCJwT4s4pJA/MzXoOLANbA1V3X4p0hAEpbSW/blieiy35EoOgEwrafxz6O/Ckj9v81rKIM28d5YFcuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:22:40.901489Z","bundle_sha256":"fb49d8906bec212db897d76a908fd5571d613ed8855faf57b10d304498c0fb75"}}