{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5T6H3EP6YQS5AZC4SFDEUEY4CC","short_pith_number":"pith:5T6H3EP6","canonical_record":{"source":{"id":"1406.7339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T00:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"f14eebcb1e39d5926ef3a9b356504c24fb343cc19f5a9bc21dc497a0a3741335","abstract_canon_sha256":"6aeeefe1faa19db07730f579ee0a745c41df43c7b99c105695e19cbe816cda6d"},"schema_version":"1.0"},"canonical_sha256":"ecfc7d91fec425d0645c91464a131c10ab78a34a06bb277b0476cd0308ce766e","source":{"kind":"arxiv","id":"1406.7339","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7339","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7339v2","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7339","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"5T6H3EP6YQS5","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5T6H3EP6YQS5AZC4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5T6H3EP6","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5T6H3EP6YQS5AZC4SFDEUEY4CC","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T00:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"f14eebcb1e39d5926ef3a9b356504c24fb343cc19f5a9bc21dc497a0a3741335","abstract_canon_sha256":"6aeeefe1faa19db07730f579ee0a745c41df43c7b99c105695e19cbe816cda6d"},"schema_version":"1.0"},"canonical_sha256":"ecfc7d91fec425d0645c91464a131c10ab78a34a06bb277b0476cd0308ce766e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:45.045144Z","signature_b64":"bH1Y8Or4KYKBwiMg/22TVCzdu+WBnjqcWeIpJhNYRK4ObiJDVjYV/Sl1ye4p0MfEmT1PAA+Risq/k7x0z4cRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecfc7d91fec425d0645c91464a131c10ab78a34a06bb277b0476cd0308ce766e","last_reissued_at":"2026-05-18T02:43:45.044528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:45.044528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7339","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqO2pcropl+fMzlMd3BoLPPBqB6naRtb9jb1P1wyXDZ0iojA8+4LsPeM2BEXBxaPuHrjpHoBo+RvkzxFUjj6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:06:22.870978Z"},"content_sha256":"9dbcd91daa8f3375e295bfc90d5d49c11adb1dfa8388a3a2ba97879c9617e99c","schema_version":"1.0","event_id":"sha256:9dbcd91daa8f3375e295bfc90d5d49c11adb1dfa8388a3a2ba97879c9617e99c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5T6H3EP6YQS5AZC4SFDEUEY4CC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block Kaczmarz Method with Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Deanna Needell, Jonathan Briskman","submitted_at":"2014-06-28T00:54:07Z","abstract_excerpt":"The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell and Tropp provided an analysis of a block version of the method for systems of linear equations. This paper considers the use of a block type method for systems of mixed equalities and inequalities, bridging these two bodies of work. We show that utilizing a matrix paving over the equalities of the system can lead to significantly improved convergence, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7339","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Db+HyTmyUyxpIte5q1nz4iLHSoa/Ntqz8bxYi+sc1Plyd4lTCpP+PyPsAqOZqRb39YbVlEFRhtAyyV7HoFyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:06:22.871674Z"},"content_sha256":"b1d00adc1070d602da68b2df3b9f5000090de25a0d5ee7264d84901eb4fc7530","schema_version":"1.0","event_id":"sha256:b1d00adc1070d602da68b2df3b9f5000090de25a0d5ee7264d84901eb4fc7530"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/bundle.json","state_url":"https://pith.science/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T15:06:22Z","links":{"resolver":"https://pith.science/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC","bundle":"https://pith.science/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/bundle.json","state":"https://pith.science/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5T6H3EP6YQS5AZC4SFDEUEY4CC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5T6H3EP6YQS5AZC4SFDEUEY4CC","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":"6aeeefe1faa19db07730f579ee0a745c41df43c7b99c105695e19cbe816cda6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T00:54:07Z","title_canon_sha256":"f14eebcb1e39d5926ef3a9b356504c24fb343cc19f5a9bc21dc497a0a3741335"},"schema_version":"1.0","source":{"id":"1406.7339","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7339","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7339v2","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7339","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"5T6H3EP6YQS5","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5T6H3EP6YQS5AZC4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5T6H3EP6","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:b1d00adc1070d602da68b2df3b9f5000090de25a0d5ee7264d84901eb4fc7530","target":"graph","created_at":"2026-05-18T02:43:45Z","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":"The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell and Tropp provided an analysis of a block version of the method for systems of linear equations. This paper considers the use of a block type method for systems of mixed equalities and inequalities, bridging these two bodies of work. We show that utilizing a matrix paving over the equalities of the system can lead to significantly improved convergence, and ","authors_text":"Deanna Needell, Jonathan Briskman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T00:54:07Z","title":"Block Kaczmarz Method with Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7339","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":"sha256:9dbcd91daa8f3375e295bfc90d5d49c11adb1dfa8388a3a2ba97879c9617e99c","target":"record","created_at":"2026-05-18T02:43:45Z","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":"6aeeefe1faa19db07730f579ee0a745c41df43c7b99c105695e19cbe816cda6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T00:54:07Z","title_canon_sha256":"f14eebcb1e39d5926ef3a9b356504c24fb343cc19f5a9bc21dc497a0a3741335"},"schema_version":"1.0","source":{"id":"1406.7339","kind":"arxiv","version":2}},"canonical_sha256":"ecfc7d91fec425d0645c91464a131c10ab78a34a06bb277b0476cd0308ce766e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecfc7d91fec425d0645c91464a131c10ab78a34a06bb277b0476cd0308ce766e","first_computed_at":"2026-05-18T02:43:45.044528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:45.044528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bH1Y8Or4KYKBwiMg/22TVCzdu+WBnjqcWeIpJhNYRK4ObiJDVjYV/Sl1ye4p0MfEmT1PAA+Risq/k7x0z4cRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:45.045144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7339","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dbcd91daa8f3375e295bfc90d5d49c11adb1dfa8388a3a2ba97879c9617e99c","sha256:b1d00adc1070d602da68b2df3b9f5000090de25a0d5ee7264d84901eb4fc7530"],"state_sha256":"d2622a3841d1e2b3c2af70377ed8afc8313a0683fefff7e2b36433416a5e322c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySE8KFKtR9WPrqCbPtobmqAHOoBwCc1lwBgLPE2rW1MJXegydiamCCM7Rro3wjzV/Nf7HWZGSkFM/EEQkZ4kCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:06:22.874696Z","bundle_sha256":"2dde6eee103ae4bbf1f8e30aeed79e504ea940335d66b30a96415ad1b6883b9e"}}