{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q4HX5VX3BRQOTKPK7XRCGMKYLW","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":"88f7c50bfd49c7de465b8ab29bade17be1446f65ca498560508110a7d1292a6a","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T14:39:09Z","title_canon_sha256":"658eea9d766ce77b49decf84ddfebae5b94d695778e563265189cb193ec72ce4"},"schema_version":"1.0","source":{"id":"1305.6818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6818","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6818v1","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6818","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"Q4HX5VX3BRQO","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q4HX5VX3BRQOTKPK","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q4HX5VX3","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:159bff00e654db828aa85e34904d95ba4dee82e1bee990b87a4b9df47ec8f187","target":"graph","created_at":"2026-05-18T01:49:40Z","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 the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned treatment of the uncertainty space. The construction of the coupled domain solution is achieved though a sequence of approximations with respect to the dimensionality of the random inputs associated with each individual sub-domain and not the combined dimensionality, hence drastically reducing the overall computational cost. The coupling between the sub-dom","authors_text":"Alireza Doostan, Hermann G. Matthies, Mohammad Hadigol, Rainer Niekamp","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T14:39:09Z","title":"Partitioned treatment of uncertainty in coupled domain problems: A separated representation approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6818","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:ab49a9d20a5f0bf00aed7da6d6963400c00bd220caf8e50b6049f102e8e19c43","target":"record","created_at":"2026-05-18T01:49:40Z","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":"88f7c50bfd49c7de465b8ab29bade17be1446f65ca498560508110a7d1292a6a","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T14:39:09Z","title_canon_sha256":"658eea9d766ce77b49decf84ddfebae5b94d695778e563265189cb193ec72ce4"},"schema_version":"1.0","source":{"id":"1305.6818","kind":"arxiv","version":1}},"canonical_sha256":"870f7ed6fb0c60e9a9eafde22331585d8649db4a88c742c96d203e49f08c1235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"870f7ed6fb0c60e9a9eafde22331585d8649db4a88c742c96d203e49f08c1235","first_computed_at":"2026-05-18T01:49:40.207611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:40.207611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"So3aQTuT9gal7upjyPk7CdIKn5PVaTOh8CWd392jmzIzw7cFD7L/hr+O0o/Kz4sHpjY7HmpfAxKaRXAeZOY+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:40.208377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab49a9d20a5f0bf00aed7da6d6963400c00bd220caf8e50b6049f102e8e19c43","sha256:159bff00e654db828aa85e34904d95ba4dee82e1bee990b87a4b9df47ec8f187"],"state_sha256":"7039f5c29fef48afa289b4a8872df12dfe0363c980751fc5f4ec34a0983225fd"}