{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G3X5OMZFWTJK7DHAZWTSI3TSHK","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":"4054f36bce5114fee1cc794fbedb0604a153dc535b40908ee93d22dc57b5e886","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-18T13:27:22Z","title_canon_sha256":"e4beb96e57616abdccac58baec90685c2c46bb77449f424fff16dea456946a0f"},"schema_version":"1.0","source":{"id":"1704.05331","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05331","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05331v4","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05331","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"G3X5OMZFWTJK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G3X5OMZFWTJK7DHA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G3X5OMZF","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:1dc85e99859b0d888bdecd75e4a2d8e474156760529961a6967d79ec31629d35","target":"graph","created_at":"2026-05-17T23:56:00Z","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":"A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It relies on a domain decomposition method which introduces several subdomains of interest (called patches) containing the different sources of uncertainties and non-linearities. An iterative algorithm is then introduced, which requires the solution of a sequence of linear global problems (with deterministic operators and uncertain right-hand sides), and non-l","authors_text":"Anthony Nouy (GeM), Florent Pled (MSME)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-18T13:27:22Z","title":"A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05331","kind":"arxiv","version":4},"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":"sha256:9f474cf1438f9c5752901994c44870d4904aaeb1791467f943806dfab821a44d","target":"record","created_at":"2026-05-17T23:56:00Z","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":"4054f36bce5114fee1cc794fbedb0604a153dc535b40908ee93d22dc57b5e886","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-18T13:27:22Z","title_canon_sha256":"e4beb96e57616abdccac58baec90685c2c46bb77449f424fff16dea456946a0f"},"schema_version":"1.0","source":{"id":"1704.05331","kind":"arxiv","version":4}},"canonical_sha256":"36efd73325b4d2af8ce0cda7246e723ab71bbca620ba7a0b4a0744980b29e35b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36efd73325b4d2af8ce0cda7246e723ab71bbca620ba7a0b4a0744980b29e35b","first_computed_at":"2026-05-17T23:56:00.361624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.361624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/bu1MIbiTgS/RWRkWnxyeBdLEI0pAhMDW6pvf7xk0yxeEBF56RUymXShT2/1SSsG80/hZfHPO2i/wBaKmzkQBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.362379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05331","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f474cf1438f9c5752901994c44870d4904aaeb1791467f943806dfab821a44d","sha256:1dc85e99859b0d888bdecd75e4a2d8e474156760529961a6967d79ec31629d35"],"state_sha256":"efe91439080941e1f143ecbded62eb7f1ce35e0d8dc375be433cc60f87e65f49"}