{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q4HX5VX3BRQOTKPK7XRCGMKYLW","short_pith_number":"pith:Q4HX5VX3","canonical_record":{"source":{"id":"1305.6818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T14:39:09Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"658eea9d766ce77b49decf84ddfebae5b94d695778e563265189cb193ec72ce4","abstract_canon_sha256":"88f7c50bfd49c7de465b8ab29bade17be1446f65ca498560508110a7d1292a6a"},"schema_version":"1.0"},"canonical_sha256":"870f7ed6fb0c60e9a9eafde22331585d8649db4a88c742c96d203e49f08c1235","source":{"kind":"arxiv","id":"1305.6818","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q4HX5VX3BRQOTKPK7XRCGMKYLW","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T14:39:09Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"658eea9d766ce77b49decf84ddfebae5b94d695778e563265189cb193ec72ce4","abstract_canon_sha256":"88f7c50bfd49c7de465b8ab29bade17be1446f65ca498560508110a7d1292a6a"},"schema_version":"1.0"},"canonical_sha256":"870f7ed6fb0c60e9a9eafde22331585d8649db4a88c742c96d203e49f08c1235","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:40.208377Z","signature_b64":"So3aQTuT9gal7upjyPk7CdIKn5PVaTOh8CWd392jmzIzw7cFD7L/hr+O0o/Kz4sHpjY7HmpfAxKaRXAeZOY+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"870f7ed6fb0c60e9a9eafde22331585d8649db4a88c742c96d203e49f08c1235","last_reissued_at":"2026-05-18T01:49:40.207611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:40.207611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6818","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJZ39K9UVr+M23ET/UmNj39NBDatcXh57YWx/CmIKL+K5A8xiMhfOusgZGuMv/LACoJTNB3ph7bo+R54bmsIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:35:16.353168Z"},"content_sha256":"ab49a9d20a5f0bf00aed7da6d6963400c00bd220caf8e50b6049f102e8e19c43","schema_version":"1.0","event_id":"sha256:ab49a9d20a5f0bf00aed7da6d6963400c00bd220caf8e50b6049f102e8e19c43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q4HX5VX3BRQOTKPK7XRCGMKYLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partitioned treatment of uncertainty in coupled domain problems: A separated representation approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Alireza Doostan, Hermann G. Matthies, Mohammad Hadigol, Rainer Niekamp","submitted_at":"2013-05-29T14:39:09Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6818","kind":"arxiv","version":1},"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":"2026-05-18T01:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jB2sBm5vU3vHxA7UXHWOzQyDoFGvQVd7M/fpDXLAyfnH9SfGssbw8SCvZEGT3AIVvLXnQ6Dd/rib/A5Mz/m+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:35:16.353546Z"},"content_sha256":"159bff00e654db828aa85e34904d95ba4dee82e1bee990b87a4b9df47ec8f187","schema_version":"1.0","event_id":"sha256:159bff00e654db828aa85e34904d95ba4dee82e1bee990b87a4b9df47ec8f187"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/bundle.json","state_url":"https://pith.science/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/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":"2026-06-06T02:35:16Z","links":{"resolver":"https://pith.science/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW","bundle":"https://pith.science/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/bundle.json","state":"https://pith.science/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4HX5VX3BRQOTKPK7XRCGMKYLW/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yw+3CKv7/L02dsvj1mP3K2EhB9epekyZcUzCfT6OXTmI+Z1rMX0qcYooWLAik+lF5AAD+409W/OOymUElZ2ECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:35:16.355544Z","bundle_sha256":"bcb54d54cacca1cf01114b91df626604fd6dc5ac84a09a58404c6ea40266b86e"}}