{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K4LI3JPFOEUR3BJ6N7PH3S6YZU","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":"0226b92536d9c27872198fe5da2537593cb4f1c1db80d9f3dbf56c7f542aa457","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-07T10:12:36Z","title_canon_sha256":"004a4e2dcae9135550b5b3575ec4789ca9da3d593ff1254e73d5485ae76a52d9"},"schema_version":"1.0","source":{"id":"1704.02167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02167","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02167v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02167","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"K4LI3JPFOEUR","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K4LI3JPFOEUR3BJ6","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K4LI3JPF","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:79918fd4f3427f7f8bbf02e9cba6dfc1f6a8c734c7ed7e4f8f6a4995c1b94e5d","target":"graph","created_at":"2026-05-17T23:43:18Z","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 consider generalizations of the Sylvester matrix equation, consisting of the sum of a Sylvester operator and a linear operator $\\Pi$ with a particular structure. More precisely, the commutator of the matrix coefficients of the operator $\\Pi$ and the Sylvester operator coefficients are assumed to be matrices with low rank. We show (under certain additional conditions) low-rank approximability of this problem, i.e., the solution to this matrix equation can be approximated with a low-rank matrix. Projection methods have successfully been used to solve other matrix equations with low-rank appro","authors_text":"Davide Palitta, Elias Jarlebring, Emil Ringh, Giampaolo Mele","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-07T10:12:36Z","title":"Krylov methods for low-rank commuting generalized Sylvester equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02167","kind":"arxiv","version":2},"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":"sha256:0e289db44d71e72527385b9dee664fe71bef0557522504611f72582853ff1004","target":"record","created_at":"2026-05-17T23:43:18Z","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":"0226b92536d9c27872198fe5da2537593cb4f1c1db80d9f3dbf56c7f542aa457","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-07T10:12:36Z","title_canon_sha256":"004a4e2dcae9135550b5b3575ec4789ca9da3d593ff1254e73d5485ae76a52d9"},"schema_version":"1.0","source":{"id":"1704.02167","kind":"arxiv","version":2}},"canonical_sha256":"57168da5e571291d853e6fde7dcbd8cd3fadc5a8feeb67460964d9f968770006","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57168da5e571291d853e6fde7dcbd8cd3fadc5a8feeb67460964d9f968770006","first_computed_at":"2026-05-17T23:43:18.644531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.644531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cV6of5eyaoWcuQ2moZgazkeHkBjhKwLxsjOsTdijkLq6Q4bLwISakWou7zwSEZ0lQIl22W8bqoFcFlqrYk5GCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.645185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e289db44d71e72527385b9dee664fe71bef0557522504611f72582853ff1004","sha256:79918fd4f3427f7f8bbf02e9cba6dfc1f6a8c734c7ed7e4f8f6a4995c1b94e5d"],"state_sha256":"7fae00beb01049ae48c4cd8942ca67c067fbde3bc14a37fc061f985f4c21f198"}