{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EZ7MJQ3RRLCQUD2DBCYT2L6WRC","short_pith_number":"pith:EZ7MJQ3R","canonical_record":{"source":{"id":"1511.05362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-11-17T11:58:24Z","cross_cats_sorted":[],"title_canon_sha256":"63e49a908af774cc99d36135a3c6818183eda8906ae53024494f002b1101fac0","abstract_canon_sha256":"21d81342646408d44a23986f1e5e932470c50b1caa3cb4fcc4b578e3c18e4f51"},"schema_version":"1.0"},"canonical_sha256":"267ec4c3718ac50a0f4308b13d2fd688b521930cd8c7b1479590c2daa7d9c7a6","source":{"kind":"arxiv","id":"1511.05362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05362","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05362v2","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05362","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"EZ7MJQ3RRLCQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EZ7MJQ3RRLCQUD2D","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EZ7MJQ3R","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EZ7MJQ3RRLCQUD2DBCYT2L6WRC","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-11-17T11:58:24Z","cross_cats_sorted":[],"title_canon_sha256":"63e49a908af774cc99d36135a3c6818183eda8906ae53024494f002b1101fac0","abstract_canon_sha256":"21d81342646408d44a23986f1e5e932470c50b1caa3cb4fcc4b578e3c18e4f51"},"schema_version":"1.0"},"canonical_sha256":"267ec4c3718ac50a0f4308b13d2fd688b521930cd8c7b1479590c2daa7d9c7a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:30.957398Z","signature_b64":"zhvFmBq6/0un8qIh9cD2aQK0aD+t3syPehqPoJ1qkpI/mnhYnHQ+zUDgyT18Gj6uW05A/HGzMA8P/phd63EIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267ec4c3718ac50a0f4308b13d2fd688b521930cd8c7b1479590c2daa7d9c7a6","last_reissued_at":"2026-05-18T01:26:30.956723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:30.956723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05362","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":"2026-05-18T01:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/COlDsN0uw7teympsAd2nDhapUYwo9rkOA3YJNIUMqYPElRphNqst+FfJVYSY4GZVtuAfaeQilsgh5kmZNbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:03.550707Z"},"content_sha256":"7e83957d12a01b7bb453af0fcf89eb8218f3a9c641912a0be242d010ab6714e4","schema_version":"1.0","event_id":"sha256:7e83957d12a01b7bb453af0fcf89eb8218f3a9c641912a0be242d010ab6714e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EZ7MJQ3RRLCQUD2DBCYT2L6WRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accelerating Random Kaczmarz Algorithm Based on Clustering Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Haishan Ye, Kaichun Mo, Yujun Li","submitted_at":"2015-11-17T11:58:24Z","abstract_excerpt":"Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05362","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":"2026-05-18T01:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6L4y+QHs80l2AypigApig+uaI9d28Eq6jI+dn9MnuHFZ5R9VGs68ZjXwoW49ek9moY0r7qmG+awknqGgFZPgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:03.551356Z"},"content_sha256":"c7fe294a623f90652f3f381b1043c553c215789a2ccb4fcdf0fa9313a03f31c5","schema_version":"1.0","event_id":"sha256:c7fe294a623f90652f3f381b1043c553c215789a2ccb4fcdf0fa9313a03f31c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/bundle.json","state_url":"https://pith.science/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/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":"2026-06-10T22:32:03Z","links":{"resolver":"https://pith.science/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC","bundle":"https://pith.science/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/bundle.json","state":"https://pith.science/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZ7MJQ3RRLCQUD2DBCYT2L6WRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EZ7MJQ3RRLCQUD2DBCYT2L6WRC","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":"21d81342646408d44a23986f1e5e932470c50b1caa3cb4fcc4b578e3c18e4f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-11-17T11:58:24Z","title_canon_sha256":"63e49a908af774cc99d36135a3c6818183eda8906ae53024494f002b1101fac0"},"schema_version":"1.0","source":{"id":"1511.05362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05362","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05362v2","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05362","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"EZ7MJQ3RRLCQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EZ7MJQ3RRLCQUD2D","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EZ7MJQ3R","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:c7fe294a623f90652f3f381b1043c553c215789a2ccb4fcdf0fa9313a03f31c5","target":"graph","created_at":"2026-05-18T01:26:30Z","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":"Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma.","authors_text":"Haishan Ye, Kaichun Mo, Yujun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-11-17T11:58:24Z","title":"Accelerating Random Kaczmarz Algorithm Based on Clustering Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05362","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":"sha256:7e83957d12a01b7bb453af0fcf89eb8218f3a9c641912a0be242d010ab6714e4","target":"record","created_at":"2026-05-18T01:26:30Z","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":"21d81342646408d44a23986f1e5e932470c50b1caa3cb4fcc4b578e3c18e4f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-11-17T11:58:24Z","title_canon_sha256":"63e49a908af774cc99d36135a3c6818183eda8906ae53024494f002b1101fac0"},"schema_version":"1.0","source":{"id":"1511.05362","kind":"arxiv","version":2}},"canonical_sha256":"267ec4c3718ac50a0f4308b13d2fd688b521930cd8c7b1479590c2daa7d9c7a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"267ec4c3718ac50a0f4308b13d2fd688b521930cd8c7b1479590c2daa7d9c7a6","first_computed_at":"2026-05-18T01:26:30.956723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:30.956723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhvFmBq6/0un8qIh9cD2aQK0aD+t3syPehqPoJ1qkpI/mnhYnHQ+zUDgyT18Gj6uW05A/HGzMA8P/phd63EIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:30.957398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e83957d12a01b7bb453af0fcf89eb8218f3a9c641912a0be242d010ab6714e4","sha256:c7fe294a623f90652f3f381b1043c553c215789a2ccb4fcdf0fa9313a03f31c5"],"state_sha256":"9fe72db5a0b16f8572737981c24b54f0766e54d4bb425062de7f3be2223d493a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVcUZNzKKEVQaJFkMyMpV+utsD/IHm6RtqMWW63YUqKd02KKQpR8QtHghLn15KoYa53dSd6E9xP+ZhCnta3mAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:32:03.555243Z","bundle_sha256":"7e4fc259bfb24502ad899f3cbfaaf4655e8bc566eb3007bde1de98b6b38bea28"}}