{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YZNYIYHM2GHMF6QF6T2GR6A7WX","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":"320544be0afd222aa211c1ba7c7f4635756db4ee72f1887dee3406b0cd1caa5c","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-29T19:16:51Z","title_canon_sha256":"e4b3153f90ca2305f9367eef67447abf6557d5cf9681ddfa2e541ebae96559a4"},"schema_version":"1.0","source":{"id":"1608.08184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08184","created_at":"2026-06-04T18:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08184v1","created_at":"2026-06-04T18:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08184","created_at":"2026-06-04T18:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"YZNYIYHM2GHM","created_at":"2026-06-04T18:09:58Z"},{"alias_kind":"pith_short_16","alias_value":"YZNYIYHM2GHMF6QF","created_at":"2026-06-04T18:09:58Z"},{"alias_kind":"pith_short_8","alias_value":"YZNYIYHM","created_at":"2026-06-04T18:09:58Z"}],"graph_snapshots":[{"event_id":"sha256:9b919ff58c931bc7e011703a95379417e5738ea5b50feb1bfa1ddf3117ff16ae","target":"graph","created_at":"2026-06-04T18:09:58Z","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/1608.08184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and efficient preconditioning strategy for solving these systems. Drawing on parabolic inf-sup theory, we first construct a left preconditioner that transforms the linear system to a symmetric positive definite problem to be solved by the preconditioned conjugate gradient algorithm. We then prove that the transformed system can be further preconditioned by an ideal ","authors_text":"Iain Smears","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-29T19:16:51Z","title":"Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08184","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":"sha256:004d5f90f33fad17e3eaa758049529cbbb427abbcd14da90c270eb0c6caf1166","target":"record","created_at":"2026-06-04T18:09:58Z","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":"320544be0afd222aa211c1ba7c7f4635756db4ee72f1887dee3406b0cd1caa5c","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-29T19:16:51Z","title_canon_sha256":"e4b3153f90ca2305f9367eef67447abf6557d5cf9681ddfa2e541ebae96559a4"},"schema_version":"1.0","source":{"id":"1608.08184","kind":"arxiv","version":1}},"canonical_sha256":"c65b8460ecd18ec2fa05f4f468f81fb5c71e23b6f0b2bbb0029a676bd05f8e88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65b8460ecd18ec2fa05f4f468f81fb5c71e23b6f0b2bbb0029a676bd05f8e88","first_computed_at":"2026-06-04T18:09:58.556822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:09:58.556822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXXVHsVj2oYf/9mJ+E+WC7AlmGrrrRZ+CFoTl5kQQGMSA8zaCnP5+RdB6AFRjphoiHGyDwgRBjm8SVT0n2x9Dg==","signature_status":"signed_v1","signed_at":"2026-06-04T18:09:58.557275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:004d5f90f33fad17e3eaa758049529cbbb427abbcd14da90c270eb0c6caf1166","sha256:9b919ff58c931bc7e011703a95379417e5738ea5b50feb1bfa1ddf3117ff16ae"],"state_sha256":"4e8aa116fa60b865b2acdebab18f23eade610ec2e0dbba317c75ebbc4e57f481"}