{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:V5YPS6DT4YWKDE2AXE5TWFST5E","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":"90732bce141e671d3d23cb4d242ee6ad5c254b0337255846daaa041bbc618219","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T12:46:26Z","title_canon_sha256":"6291279c3027eb18116cb30bc14703ad6cc37ce5c7ce2bea21dedbfa73db68a8"},"schema_version":"1.0","source":{"id":"2506.02816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02816","created_at":"2026-07-05T11:15:09Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02816v1","created_at":"2026-07-05T11:15:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02816","created_at":"2026-07-05T11:15:09Z"},{"alias_kind":"pith_short_12","alias_value":"V5YPS6DT4YWK","created_at":"2026-07-05T11:15:09Z"},{"alias_kind":"pith_short_16","alias_value":"V5YPS6DT4YWKDE2A","created_at":"2026-07-05T11:15:09Z"},{"alias_kind":"pith_short_8","alias_value":"V5YPS6DT","created_at":"2026-07-05T11:15:09Z"}],"graph_snapshots":[{"event_id":"sha256:89f710390ae491d696fd93a3e0a9b013f5373d5e46bddb836e6ee48e054fa1fc","target":"graph","created_at":"2026-07-05T11:15:09Z","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/2506.02816/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \\times 3$ block systems [Bradley and Greif, IMA J.\\ Numer. Anal. 43 (2023)] and for $4 \\times 4$ systems [Pearson and Potschka, IMA J. Numer. Anal. 44 (2024)] to an arbitrary number of blocks. Moreover, our results generalize the bounds in [Sogn and Zulehner, IMA J. Numer. Anal. 39 (2018)], developed for an arbitrary number of blocks with null diagonal blocks. Extension to the bounds when the Schur complements are approx","authors_text":"A. Martinez, A. Potschka, J.W. Pearson, L. Bergamaschi","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T12:46:26Z","title":"Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02816","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":"sha256:79e4a517060ca2915f31b24ed808683e8ad98c2b63c44d34806e45d58f003267","target":"record","created_at":"2026-07-05T11:15:09Z","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":"90732bce141e671d3d23cb4d242ee6ad5c254b0337255846daaa041bbc618219","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T12:46:26Z","title_canon_sha256":"6291279c3027eb18116cb30bc14703ad6cc37ce5c7ce2bea21dedbfa73db68a8"},"schema_version":"1.0","source":{"id":"2506.02816","kind":"arxiv","version":1}},"canonical_sha256":"af70f97873e62ca19340b93b3b1653e934fc45fc8a3479e2b61dc0428eeb1fe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af70f97873e62ca19340b93b3b1653e934fc45fc8a3479e2b61dc0428eeb1fe6","first_computed_at":"2026-07-05T11:15:09.712499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:09.712499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ydc4gJgHFpZ451WhQq0KR56IwuJeC/tPNpEdfEX8bH03QM1FsIwXdxfV9Vg5JST2EGgPL3bu2tJDDnIDmj/tDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:09.713082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79e4a517060ca2915f31b24ed808683e8ad98c2b63c44d34806e45d58f003267","sha256:89f710390ae491d696fd93a3e0a9b013f5373d5e46bddb836e6ee48e054fa1fc"],"state_sha256":"076cb5e2d8ae8e849e2118b9850ff46d2776a11e7fbf10cd6f9f8eb2083fa0f9"}