{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B43WM74NCZJZKBR7B36OJFWVUA","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":"22f706e5215ae5ed960e186cb1f1b29e603d7cb08fe676c8d70ebe9b63ded98e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-16T16:21:33Z","title_canon_sha256":"f323fe5905676e03bb0131c5988e67b9b2d0a38f5123470d98e27c5bbae113d8"},"schema_version":"1.0","source":{"id":"2607.15171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15171","created_at":"2026-07-17T01:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15171v1","created_at":"2026-07-17T01:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15171","created_at":"2026-07-17T01:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"B43WM74NCZJZ","created_at":"2026-07-17T01:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"B43WM74NCZJZKBR7","created_at":"2026-07-17T01:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"B43WM74N","created_at":"2026-07-17T01:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:4fbaa478d7989ea41686466da2e5dfed70c592867b12514135084f8a0fa4c681","target":"graph","created_at":"2026-07-17T01:22:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.15171/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many computational models arising in science and engineering exhibit a multiscale structure that makes the assembly or direct solution of the global problem computationally prohibitive. Domain Decomposition (DD) methods overcome this limitation by replacing the global problem with a sequence of coupled local problems, whose iterative solution reconstructs the global response. This work introduces a method in the family of Domain Decomposition Reduced Order Models (DD-ROMs), based on the observation that DD naturally localizes not only the solution operator but also its geometric and parametric","authors_text":"Nunzio Dimola, Paolo Zunino, Piermario Vitullo","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-16T16:21:33Z","title":"Multiscale Mixed-Dimensional Simulation via Domain Decomposition and Non-Intrusive Neural Model Order Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15171","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":"sha256:0dcbe61709a9ef563f00e5dd1bd98569fd9b97b5126003e09504ca1433993f23","target":"record","created_at":"2026-07-17T01:22:12Z","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":"22f706e5215ae5ed960e186cb1f1b29e603d7cb08fe676c8d70ebe9b63ded98e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-16T16:21:33Z","title_canon_sha256":"f323fe5905676e03bb0131c5988e67b9b2d0a38f5123470d98e27c5bbae113d8"},"schema_version":"1.0","source":{"id":"2607.15171","kind":"arxiv","version":1}},"canonical_sha256":"0f37667f8d165395063f0efce496d5a01d602e4c06292cab03c2e29d061d20ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f37667f8d165395063f0efce496d5a01d602e4c06292cab03c2e29d061d20ab","first_computed_at":"2026-07-17T01:22:12.787436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:22:12.787436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t9kRMODVrwpw5EuvtEhpyVPQT6raSo/9Y+mV/sOrulYrN733yhUYf3rFvUu96PVqntMg6Qdm30hEkX8lmscMAA==","signature_status":"signed_v1","signed_at":"2026-07-17T01:22:12.788195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dcbe61709a9ef563f00e5dd1bd98569fd9b97b5126003e09504ca1433993f23","sha256:4fbaa478d7989ea41686466da2e5dfed70c592867b12514135084f8a0fa4c681"],"state_sha256":"1ba0e115625d228164684dd8023b6892110ca668e2a371fc1570fb5575f569da"}