{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GRF33LKSWX2RW5XNLBSU7SP5GT","short_pith_number":"pith:GRF33LKS","canonical_record":{"source":{"id":"1912.00771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-28T07:13:03Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"c068b111d54cd2db06892ae0c8adc363448eb268ab3638b0d213183b874a36a6","abstract_canon_sha256":"ff4d8081a555d368b773c13186a4c5238653cb2c47ee02073aa072130f9b7067"},"schema_version":"1.0"},"canonical_sha256":"344bbdad52b5f51b76ed58654fc9fd34ffe4f7baffc3072eb82a59ede8764400","source":{"kind":"arxiv","id":"1912.00771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00771","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00771v1","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00771","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"GRF33LKSWX2R","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_16","alias_value":"GRF33LKSWX2RW5XN","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_8","alias_value":"GRF33LKS","created_at":"2026-07-05T00:23:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GRF33LKSWX2RW5XNLBSU7SP5GT","target":"record","payload":{"canonical_record":{"source":{"id":"1912.00771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-28T07:13:03Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"c068b111d54cd2db06892ae0c8adc363448eb268ab3638b0d213183b874a36a6","abstract_canon_sha256":"ff4d8081a555d368b773c13186a4c5238653cb2c47ee02073aa072130f9b7067"},"schema_version":"1.0"},"canonical_sha256":"344bbdad52b5f51b76ed58654fc9fd34ffe4f7baffc3072eb82a59ede8764400","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:23:16.719990Z","signature_b64":"xh0D7aOVTk253mVmrWeWF0CIKbaspGKCtvHmWlWoQkhT5MXQtXrQxbeiikATYv4zcCUY/Cef382l7LGVW3JRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"344bbdad52b5f51b76ed58654fc9fd34ffe4f7baffc3072eb82a59ede8764400","last_reissued_at":"2026-07-05T00:23:16.719548Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:23:16.719548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.00771","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8a7NMJYarAoM07auxQMRCVtacZl9/Q6MqwMtetrGOs5ook0XR+Agl5Fn/RJb6VOwQYjveFsoiW5yvTh3i9/kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:30:48.921548Z"},"content_sha256":"4f8fd4219486f16c17358b413853d27c48ebde02bcdf66c2f37c155f4e0c4895","schema_version":"1.0","event_id":"sha256:4f8fd4219486f16c17358b413853d27c48ebde02bcdf66c2f37c155f4e0c4895"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GRF33LKSWX2RW5XNLBSU7SP5GT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sketching for Motzkin's Iterative Method for Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Deanna Needell, Elizaveta Rebrova","submitted_at":"2019-11-28T07:13:03Z","abstract_excerpt":"Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing steps that reduce the dimension of each iteration) can improve the performance of iterative methods in multiple ways, such as, to speed up the convergence of the method by fighting inner correlations of the system, or to reduce the variance incurred by the presence of noise. In the current work, we show that sketching can also help us to get better theoretical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00771","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.00771/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yT/Vf6r3wmWP8WT6iO7Zmb0rlWDXXmoVjPkasfLu7s/0AwDYorZbbpHkj0/WsEGliCZevwLI4Wo+iuNvT3AjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:30:48.922219Z"},"content_sha256":"9e8d2bfa204cf0f26d453559306b5e8d638886cc4f8e76e8a17fc48a6ceb42d0","schema_version":"1.0","event_id":"sha256:9e8d2bfa204cf0f26d453559306b5e8d638886cc4f8e76e8a17fc48a6ceb42d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/bundle.json","state_url":"https://pith.science/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/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":"2026-08-03T22:30:48Z","links":{"resolver":"https://pith.science/pith/GRF33LKSWX2RW5XNLBSU7SP5GT","bundle":"https://pith.science/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/bundle.json","state":"https://pith.science/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRF33LKSWX2RW5XNLBSU7SP5GT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GRF33LKSWX2RW5XNLBSU7SP5GT","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":"ff4d8081a555d368b773c13186a4c5238653cb2c47ee02073aa072130f9b7067","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-28T07:13:03Z","title_canon_sha256":"c068b111d54cd2db06892ae0c8adc363448eb268ab3638b0d213183b874a36a6"},"schema_version":"1.0","source":{"id":"1912.00771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00771","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00771v1","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00771","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"GRF33LKSWX2R","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_16","alias_value":"GRF33LKSWX2RW5XN","created_at":"2026-07-05T00:23:16Z"},{"alias_kind":"pith_short_8","alias_value":"GRF33LKS","created_at":"2026-07-05T00:23:16Z"}],"graph_snapshots":[{"event_id":"sha256:9e8d2bfa204cf0f26d453559306b5e8d638886cc4f8e76e8a17fc48a6ceb42d0","target":"graph","created_at":"2026-07-05T00:23:16Z","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/1912.00771/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing steps that reduce the dimension of each iteration) can improve the performance of iterative methods in multiple ways, such as, to speed up the convergence of the method by fighting inner correlations of the system, or to reduce the variance incurred by the presence of noise. In the current work, we show that sketching can also help us to get better theoretical ","authors_text":"Deanna Needell, Elizaveta Rebrova","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-28T07:13:03Z","title":"Sketching for Motzkin's Iterative Method for Linear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00771","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":"sha256:4f8fd4219486f16c17358b413853d27c48ebde02bcdf66c2f37c155f4e0c4895","target":"record","created_at":"2026-07-05T00:23:16Z","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":"ff4d8081a555d368b773c13186a4c5238653cb2c47ee02073aa072130f9b7067","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-28T07:13:03Z","title_canon_sha256":"c068b111d54cd2db06892ae0c8adc363448eb268ab3638b0d213183b874a36a6"},"schema_version":"1.0","source":{"id":"1912.00771","kind":"arxiv","version":1}},"canonical_sha256":"344bbdad52b5f51b76ed58654fc9fd34ffe4f7baffc3072eb82a59ede8764400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"344bbdad52b5f51b76ed58654fc9fd34ffe4f7baffc3072eb82a59ede8764400","first_computed_at":"2026-07-05T00:23:16.719548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:23:16.719548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xh0D7aOVTk253mVmrWeWF0CIKbaspGKCtvHmWlWoQkhT5MXQtXrQxbeiikATYv4zcCUY/Cef382l7LGVW3JRBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:23:16.719990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.00771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f8fd4219486f16c17358b413853d27c48ebde02bcdf66c2f37c155f4e0c4895","sha256:9e8d2bfa204cf0f26d453559306b5e8d638886cc4f8e76e8a17fc48a6ceb42d0"],"state_sha256":"37598d07806801d78160f80f57ff8f2c9a97fee330befed5dc2b4c45c55c80ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cBB+BX9IHBKrZc8TrNZWvbSdxv2RPfVTTmkiRkN7FkXXJ7nkOo2mBbuqyFv+QWEbb4er5JA+vx6mRT532F6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:30:48.928198Z","bundle_sha256":"e10a4e72bba66eced33d94260502be0b0e2c628d4380950a5e2cde8f730c8e77"}}