{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LT6VAGDFJTI56LYLBNKUDR4XMS","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":"653e0c54d1b010935291994d783273f2aa5c823c96da6614786e0b02020d8c51","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-15T13:49:00Z","title_canon_sha256":"04ba59270d6aff87187d0cb45804c52958d6ba1f7fe5162a1c63cd62d6428f86"},"schema_version":"1.0","source":{"id":"1908.05537","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05537","created_at":"2026-07-05T02:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05537v3","created_at":"2026-07-05T02:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05537","created_at":"2026-07-05T02:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"LT6VAGDFJTI5","created_at":"2026-07-05T02:33:52Z"},{"alias_kind":"pith_short_16","alias_value":"LT6VAGDFJTI56LYL","created_at":"2026-07-05T02:33:52Z"},{"alias_kind":"pith_short_8","alias_value":"LT6VAGDF","created_at":"2026-07-05T02:33:52Z"}],"graph_snapshots":[{"event_id":"sha256:970deddf0b55f831c54651ef097ab1a934e75d32c636e220bddc81d485ac6a7b","target":"graph","created_at":"2026-07-05T02:33:52Z","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/1908.05537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corresponding smoothing iterative method), which is based on domain decomposition techniques, and a coarse correction step, which relies on a coarse space. The coarse space must properly represent the error components that the chosen one-level method is not capable to deal with. In the literature most of the works introduced efficient coarse","authors_text":"Gabriele Ciaramella, Tommaso Vanzan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-15T13:49:00Z","title":"Spectral substructured two-level domain decomposition methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05537","kind":"arxiv","version":3},"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":"sha256:010caf1e6956582c0ffe597104cb62f8d1101d453bdd1d8934f0179defb2ad6c","target":"record","created_at":"2026-07-05T02:33:52Z","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":"653e0c54d1b010935291994d783273f2aa5c823c96da6614786e0b02020d8c51","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-15T13:49:00Z","title_canon_sha256":"04ba59270d6aff87187d0cb45804c52958d6ba1f7fe5162a1c63cd62d6428f86"},"schema_version":"1.0","source":{"id":"1908.05537","kind":"arxiv","version":3}},"canonical_sha256":"5cfd5018654cd1df2f0b0b5541c79764bcd7b552ca3281f05ce65e4e5a60c32f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cfd5018654cd1df2f0b0b5541c79764bcd7b552ca3281f05ce65e4e5a60c32f","first_computed_at":"2026-07-05T02:33:52.808965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:33:52.808965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbwwC4EyTSwRK8bs+y6AYhd2h5A9Z6V80gi6LYIi2NU0314GHhlKEQGP6NAh8aK1D9FKY/a024+oV63OxnMbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:33:52.809463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05537","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:010caf1e6956582c0ffe597104cb62f8d1101d453bdd1d8934f0179defb2ad6c","sha256:970deddf0b55f831c54651ef097ab1a934e75d32c636e220bddc81d485ac6a7b"],"state_sha256":"5622e7ec2de4e53456d1bee2fb76bc6c8b7c62434989afd1d232f3a6eb36c61a"}