{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LVYUOE24K7HHQW3F5QG6LA52Q6","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":"a01601742c3808424cad68273e8be2f53ed0e447d8ad6e09047d5ff64dae411b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-04T20:15:46Z","title_canon_sha256":"8c89ae017ad7421aaf89040b337804b41f91552790415e885c139773c8db285d"},"schema_version":"1.0","source":{"id":"1605.01418","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01418","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01418v6","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01418","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"LVYUOE24K7HH","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LVYUOE24K7HHQW3F","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LVYUOE24","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:fa5aa7079647f03267da45165df9ae11068e0a6727a313f3e756625be3d7ab07","target":"graph","created_at":"2026-05-17T23:44:23Z","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 combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. In doing so, we obtain a family of algorithms that generalize and extend both techniques. We prove several convergence results, and our computational experiments show our algorithms often outperform the original methods.","authors_text":"Deanna Needell, Jamie Haddock, Jesus De Loera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-04T20:15:46Z","title":"A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01418","kind":"arxiv","version":6},"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:eda4f85dc64d0d4c838abcd6187baa94d21fe658b81d8f05cc6cd27949b2da5e","target":"record","created_at":"2026-05-17T23:44:23Z","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":"a01601742c3808424cad68273e8be2f53ed0e447d8ad6e09047d5ff64dae411b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-04T20:15:46Z","title_canon_sha256":"8c89ae017ad7421aaf89040b337804b41f91552790415e885c139773c8db285d"},"schema_version":"1.0","source":{"id":"1605.01418","kind":"arxiv","version":6}},"canonical_sha256":"5d7147135c57ce785b65ec0de583ba8784b11a12046633509f9333625de9f534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d7147135c57ce785b65ec0de583ba8784b11a12046633509f9333625de9f534","first_computed_at":"2026-05-17T23:44:23.224975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:23.224975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aSDnUsTAAGWjAMPQg6NC7JGPYTpvhhXI8hjLNvI3LWCJNTxk8rAUXCsdL0oBBYiD/qTlnMbN9igSMSfCJr0rAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:23.225601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01418","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eda4f85dc64d0d4c838abcd6187baa94d21fe658b81d8f05cc6cd27949b2da5e","sha256:fa5aa7079647f03267da45165df9ae11068e0a6727a313f3e756625be3d7ab07"],"state_sha256":"3772220a19b4e6756b7a5a78444d8e5d5d4b49a516bf52895f66d05141c65977"}