{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SZNVKXO2JCR42Y6BJFQ2EKOV6F","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":"6001cfc402101c057290a6d56010d8ca8c8e8ec9e132479966d339e64caa378c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-23T19:56:35Z","title_canon_sha256":"de3e2294f4a0b15fea3b88929889ac5e357020eae6d6aba40441117b26e41bf2"},"schema_version":"1.0","source":{"id":"1606.07425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07425","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07425v2","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07425","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"SZNVKXO2JCR4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SZNVKXO2JCR42Y6B","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SZNVKXO2","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:7beef61b23a293cbe009b58529776322a1e1bb7b96f80347d71311dbbf0dc6d2","target":"graph","created_at":"2026-05-18T01:11:54Z","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 approximation algorithms for the problem of finding $x$ of minimal norm $\\|x\\|$ satisfying a linear system $\\mathbf{A} x = \\mathbf{b}$, where the norm $\\|\\cdot \\|$ is arbitrary and generally non-Euclidean. We show a simple general technique for composing solvers, converting iterative solvers with residual error $\\|\\mathbf{A} x - \\mathbf{b}\\| \\leq t^{-\\Omega(1)}$ into solvers with residual error $\\exp(-\\Omega(t))$, at the cost of an increase in $\\|x\\|$, by recursively invoking the solver on the residual problem $\\tilde{\\mathbf{b}} = \\mathbf{b} - \\mathbf{A} x$. Convergence of the com","authors_text":"Jonah Sherman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-23T19:56:35Z","title":"Generalized Preconditioning and Network Flow Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07425","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:c94d18abfb06c86e1ca0f92701f97ea11f64a7df52eda23af8f8dda094e9129a","target":"record","created_at":"2026-05-18T01:11:54Z","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":"6001cfc402101c057290a6d56010d8ca8c8e8ec9e132479966d339e64caa378c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-23T19:56:35Z","title_canon_sha256":"de3e2294f4a0b15fea3b88929889ac5e357020eae6d6aba40441117b26e41bf2"},"schema_version":"1.0","source":{"id":"1606.07425","kind":"arxiv","version":2}},"canonical_sha256":"965b555dda48a3cd63c14961a229d5f160d0d0da68e78529730694c54fe89e21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"965b555dda48a3cd63c14961a229d5f160d0d0da68e78529730694c54fe89e21","first_computed_at":"2026-05-18T01:11:54.375778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:54.375778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cretc+5tNzgo3ImfEqVSLK4RT7OtCTihMGYQLzhwVz85sjfQEUkyNfGp1B71UGhejSPZZUMm6/mtZxCqOPKyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:54.376114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c94d18abfb06c86e1ca0f92701f97ea11f64a7df52eda23af8f8dda094e9129a","sha256:7beef61b23a293cbe009b58529776322a1e1bb7b96f80347d71311dbbf0dc6d2"],"state_sha256":"75086db3e73cd35194c818ee3574210d70f0d13f7aa832d381094bab10464d56"}