{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UOTDMCJXIJLMXO2KQRD7P3KQF4","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":"ee9961885d0574e4cd63278af74f21860afb94b4d10fba7d61d4378f83516550","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-23T20:05:49Z","title_canon_sha256":"7810588a0437c02914e2b45b89417aab9ec77ca5b3d8d74264bc8862100b4a62"},"schema_version":"1.0","source":{"id":"1605.07198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07198","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07198v1","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07198","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"UOTDMCJXIJLM","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UOTDMCJXIJLMXO2K","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UOTDMCJX","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:360d289ae86753d2c245f51350c9143a90864a08b768c1d48772294bf072b642","target":"graph","created_at":"2026-05-18T00:18:57Z","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":"We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical experiments.","authors_text":"Joris C. G. Verschaeve, Kent-Andre Mardal, Magne Nordaas, Mikael Mortensen, Miroslav Kuchta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-23T20:05:49Z","title":"Efficient preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07198","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":"sha256:7d91973e575de654ba259a608bea450e98f2627b689a246702a5bf34b5d18201","target":"record","created_at":"2026-05-18T00:18:57Z","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":"ee9961885d0574e4cd63278af74f21860afb94b4d10fba7d61d4378f83516550","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-23T20:05:49Z","title_canon_sha256":"7810588a0437c02914e2b45b89417aab9ec77ca5b3d8d74264bc8862100b4a62"},"schema_version":"1.0","source":{"id":"1605.07198","kind":"arxiv","version":1}},"canonical_sha256":"a3a63609374256cbbb4a8447f7ed502f19191ac3049ee3768044babac616b4a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3a63609374256cbbb4a8447f7ed502f19191ac3049ee3768044babac616b4a3","first_computed_at":"2026-05-18T00:18:57.198447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:57.198447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DI6JNz8BiUIqaLpN8za3VSCxDVQG800i16T785NRu95jDr3blTTbZ5pyEXwj5nmmoosNEwBMZqxt99dt0K2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:57.198962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d91973e575de654ba259a608bea450e98f2627b689a246702a5bf34b5d18201","sha256:360d289ae86753d2c245f51350c9143a90864a08b768c1d48772294bf072b642"],"state_sha256":"95d73c4d449be3389e9de66e96e21c0a48898ff2831f50acb023645aa9e7a469"}