{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CGPXHFUCKVEAO4K2VIPVT3LCEZ","short_pith_number":"pith:CGPXHFUC","canonical_record":{"source":{"id":"2510.02156","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-10-02T16:08:27Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4c8efcbb4bcbf7da08b5cc8dfaf5a9edf20de6ef92179feeabf3813cd3fcb0f9","abstract_canon_sha256":"be4c9335e9128958e344d7ae55a40dd63d8e00bd548ae637199dc43d2b042e53"},"schema_version":"1.0"},"canonical_sha256":"119f739682554807715aaa1f59ed62266f154aeaaa750a472dae9c081783e25b","source":{"kind":"arxiv","id":"2510.02156","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.02156","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"arxiv_version","alias_value":"2510.02156v2","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.02156","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_12","alias_value":"CGPXHFUCKVEA","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_16","alias_value":"CGPXHFUCKVEAO4K2","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_8","alias_value":"CGPXHFUC","created_at":"2026-06-19T16:09:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CGPXHFUCKVEAO4K2VIPVT3LCEZ","target":"record","payload":{"canonical_record":{"source":{"id":"2510.02156","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-10-02T16:08:27Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4c8efcbb4bcbf7da08b5cc8dfaf5a9edf20de6ef92179feeabf3813cd3fcb0f9","abstract_canon_sha256":"be4c9335e9128958e344d7ae55a40dd63d8e00bd548ae637199dc43d2b042e53"},"schema_version":"1.0"},"canonical_sha256":"119f739682554807715aaa1f59ed62266f154aeaaa750a472dae9c081783e25b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:09:51.445028Z","signature_b64":"a5JYyY5dILCKAaxDrySUIVbcNx6BNZAdYCynSJRknd9rObLBWjecIR76rHDjOs77iB31Yu/EytAvXHjFyb7gCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"119f739682554807715aaa1f59ed62266f154aeaaa750a472dae9c081783e25b","last_reissued_at":"2026-06-19T16:09:51.444607Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:09:51.444607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.02156","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":"2026-06-19T16:09:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jdNlsMHB/WzHknG280y10i0GD4U24JigKMDWAysPZMmJKnxJHaBH6afmuE2KQFA2IoKpIBIjhRj3+AjwS0dVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:32:33.352803Z"},"content_sha256":"5d3e99a3cd83ceb9042a24969d5878720df969bd107e3743bf761317786381aa","schema_version":"1.0","event_id":"sha256:5d3e99a3cd83ceb9042a24969d5878720df969bd107e3743bf761317786381aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CGPXHFUCKVEAO4K2VIPVT3LCEZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fast solver for ill-conditioned linear systems using randomized stable solutions of its blocks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Murugesan Venkatapathi, Suvendu Kar","submitted_at":"2025-10-02T16:08:27Z","abstract_excerpt":"We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution based on the current residual vector and effective mutual orthogonality between all blocks. The improved method provides significant gains in solving highly ill-conditioned linear systems that are either sparse, or dense least-squares problems that are significantly over/under determined. Considering the poor guarantees in effectively preconditioning iterat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.02156","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.02156/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":"2026-06-19T16:09:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2iUOFbzgUsSsNqK9Swpyk15JSJdT+a6m8wZ6PGoBpKH+XKD8J4arHTNGVrzS4vuyDepmwtDvcRh9kIlBOXoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:32:33.353186Z"},"content_sha256":"1615267389251fb81444ed8f5ab2ca2d45fbdc47717c85569fb1595a93a2e8c6","schema_version":"1.0","event_id":"sha256:1615267389251fb81444ed8f5ab2ca2d45fbdc47717c85569fb1595a93a2e8c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/bundle.json","state_url":"https://pith.science/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/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":"2026-06-24T11:32:33Z","links":{"resolver":"https://pith.science/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ","bundle":"https://pith.science/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/bundle.json","state":"https://pith.science/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGPXHFUCKVEAO4K2VIPVT3LCEZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CGPXHFUCKVEAO4K2VIPVT3LCEZ","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":"be4c9335e9128958e344d7ae55a40dd63d8e00bd548ae637199dc43d2b042e53","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-10-02T16:08:27Z","title_canon_sha256":"4c8efcbb4bcbf7da08b5cc8dfaf5a9edf20de6ef92179feeabf3813cd3fcb0f9"},"schema_version":"1.0","source":{"id":"2510.02156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.02156","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"arxiv_version","alias_value":"2510.02156v2","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.02156","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_12","alias_value":"CGPXHFUCKVEA","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_16","alias_value":"CGPXHFUCKVEAO4K2","created_at":"2026-06-19T16:09:51Z"},{"alias_kind":"pith_short_8","alias_value":"CGPXHFUC","created_at":"2026-06-19T16:09:51Z"}],"graph_snapshots":[{"event_id":"sha256:1615267389251fb81444ed8f5ab2ca2d45fbdc47717c85569fb1595a93a2e8c6","target":"graph","created_at":"2026-06-19T16:09:51Z","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/2510.02156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution based on the current residual vector and effective mutual orthogonality between all blocks. The improved method provides significant gains in solving highly ill-conditioned linear systems that are either sparse, or dense least-squares problems that are significantly over/under determined. Considering the poor guarantees in effectively preconditioning iterat","authors_text":"Murugesan Venkatapathi, Suvendu Kar","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-10-02T16:08:27Z","title":"A fast solver for ill-conditioned linear systems using randomized stable solutions of its blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.02156","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":"sha256:5d3e99a3cd83ceb9042a24969d5878720df969bd107e3743bf761317786381aa","target":"record","created_at":"2026-06-19T16:09:51Z","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":"be4c9335e9128958e344d7ae55a40dd63d8e00bd548ae637199dc43d2b042e53","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-10-02T16:08:27Z","title_canon_sha256":"4c8efcbb4bcbf7da08b5cc8dfaf5a9edf20de6ef92179feeabf3813cd3fcb0f9"},"schema_version":"1.0","source":{"id":"2510.02156","kind":"arxiv","version":2}},"canonical_sha256":"119f739682554807715aaa1f59ed62266f154aeaaa750a472dae9c081783e25b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"119f739682554807715aaa1f59ed62266f154aeaaa750a472dae9c081783e25b","first_computed_at":"2026-06-19T16:09:51.444607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:09:51.444607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5JYyY5dILCKAaxDrySUIVbcNx6BNZAdYCynSJRknd9rObLBWjecIR76rHDjOs77iB31Yu/EytAvXHjFyb7gCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:09:51.445028Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.02156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d3e99a3cd83ceb9042a24969d5878720df969bd107e3743bf761317786381aa","sha256:1615267389251fb81444ed8f5ab2ca2d45fbdc47717c85569fb1595a93a2e8c6"],"state_sha256":"cdb241fd61065edcea9adce0908b167de101854033846b5b1e0ebe2d3c1d8c07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1JJmPD97QSBngYBowKhdq8ZSxirL594Ew5XPzZHICT7MbHHAOjkMtVg5nNrH/dXooeV2Da+rFKGRK1jroneoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:32:33.355405Z","bundle_sha256":"cc64699fbe2ce5eb2063db1853ff64a3a370fbe4e94801f0cea6c7c0a9448cde"}}