{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4EKN4LKOKGWVLIJQ3PJV3RGVZZ","short_pith_number":"pith:4EKN4LKO","canonical_record":{"source":{"id":"2008.01722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-04T17:53:28Z","cross_cats_sorted":["cs.DS","cs.LG","stat.ML"],"title_canon_sha256":"9ed4768c61802420b0b1782e478487399927569d9eebaa155f21428e3f2a426e","abstract_canon_sha256":"5a77741ced62dab7ad5de5644929278d5b7040de38ddb6e7ca897b3b1d734eb2"},"schema_version":"1.0"},"canonical_sha256":"e114de2d4e51ad55a130dbd35dc4d5ce616092a822f30a955b6868af66f2a7d5","source":{"kind":"arxiv","id":"2008.01722","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01722","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01722v2","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01722","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"4EKN4LKOKGWV","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_16","alias_value":"4EKN4LKOKGWVLIJQ","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_8","alias_value":"4EKN4LKO","created_at":"2026-07-05T03:28:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4EKN4LKOKGWVLIJQ3PJV3RGVZZ","target":"record","payload":{"canonical_record":{"source":{"id":"2008.01722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-04T17:53:28Z","cross_cats_sorted":["cs.DS","cs.LG","stat.ML"],"title_canon_sha256":"9ed4768c61802420b0b1782e478487399927569d9eebaa155f21428e3f2a426e","abstract_canon_sha256":"5a77741ced62dab7ad5de5644929278d5b7040de38ddb6e7ca897b3b1d734eb2"},"schema_version":"1.0"},"canonical_sha256":"e114de2d4e51ad55a130dbd35dc4d5ce616092a822f30a955b6868af66f2a7d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:28:34.955586Z","signature_b64":"w64uEOOPwCOuaq0oMjkH0vWJ/NoTwlcadZb4LqYHLny0M+hR+JB3Be23liRqxOjLh6T6mGuoV3iJ1t6tAWjrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e114de2d4e51ad55a130dbd35dc4d5ce616092a822f30a955b6868af66f2a7d5","last_reissued_at":"2026-07-05T03:28:34.955154Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:28:34.955154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.01722","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":"2026-07-05T03:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuhzbXk7ZL6g7YgGo3CRFBX5mmFcTtJ0IrlBsnFmgENJXdnIGm2mk7uPnpm2PeYUVxtPu3IzmG+NBx5nwA43Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:16:04.894956Z"},"content_sha256":"ed40a2260d43c4565a70f4c5f6bdc02da584084544de9f9b617b7a077b9d5d67","schema_version":"1.0","event_id":"sha256:ed40a2260d43c4565a70f4c5f6bdc02da584084544de9f9b617b7a077b9d5d67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4EKN4LKOKGWVLIJQ3PJV3RGVZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast and Near-Optimal Diagonal Preconditioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Aaron Sidford, Arun Jambulapati, Christopher Musco, Jerry Li, Kevin Tian","submitted_at":"2020-08-04T17:53:28Z","abstract_excerpt":"The convergence rates of iterative methods for solving a linear system $\\mathbf{A} x = b$ typically depend on the condition number of the matrix $\\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that condition number in a computationally inexpensive way. In this paper, we revisit the decades-old problem of how to best improve $\\mathbf{A}$'s condition number by left or right diagonal rescaling. We make progress on this problem in several directions.\n  First, we provide new bounds for the classic heuristic of scaling $\\mathbf{A}$ by its diagonal values (a.k.a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01722","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/2008.01722/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":"2026-07-05T03:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+p3qxxL3FdwRV0ohzlQzGOdqCQkjKEo7Pl5IhdS1YBkI+C3ncZXMMc9/kyK2i2JYmslndxrhsVDG2SnYzvoDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:16:04.895578Z"},"content_sha256":"47412a42c4555faccdbdf000322f3e961d11a50100fb5422610c2dbba863b2d8","schema_version":"1.0","event_id":"sha256:47412a42c4555faccdbdf000322f3e961d11a50100fb5422610c2dbba863b2d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/bundle.json","state_url":"https://pith.science/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/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":"2026-08-17T16:16:04Z","links":{"resolver":"https://pith.science/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ","bundle":"https://pith.science/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/bundle.json","state":"https://pith.science/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EKN4LKOKGWVLIJQ3PJV3RGVZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4EKN4LKOKGWVLIJQ3PJV3RGVZZ","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":"5a77741ced62dab7ad5de5644929278d5b7040de38ddb6e7ca897b3b1d734eb2","cross_cats_sorted":["cs.DS","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-04T17:53:28Z","title_canon_sha256":"9ed4768c61802420b0b1782e478487399927569d9eebaa155f21428e3f2a426e"},"schema_version":"1.0","source":{"id":"2008.01722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01722","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01722v2","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01722","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"4EKN4LKOKGWV","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_16","alias_value":"4EKN4LKOKGWVLIJQ","created_at":"2026-07-05T03:28:34Z"},{"alias_kind":"pith_short_8","alias_value":"4EKN4LKO","created_at":"2026-07-05T03:28:34Z"}],"graph_snapshots":[{"event_id":"sha256:47412a42c4555faccdbdf000322f3e961d11a50100fb5422610c2dbba863b2d8","target":"graph","created_at":"2026-07-05T03:28:34Z","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/2008.01722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The convergence rates of iterative methods for solving a linear system $\\mathbf{A} x = b$ typically depend on the condition number of the matrix $\\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that condition number in a computationally inexpensive way. In this paper, we revisit the decades-old problem of how to best improve $\\mathbf{A}$'s condition number by left or right diagonal rescaling. We make progress on this problem in several directions.\n  First, we provide new bounds for the classic heuristic of scaling $\\mathbf{A}$ by its diagonal values (a.k.a","authors_text":"Aaron Sidford, Arun Jambulapati, Christopher Musco, Jerry Li, Kevin Tian","cross_cats":["cs.DS","cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-04T17:53:28Z","title":"Fast and Near-Optimal Diagonal Preconditioning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01722","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:ed40a2260d43c4565a70f4c5f6bdc02da584084544de9f9b617b7a077b9d5d67","target":"record","created_at":"2026-07-05T03:28:34Z","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":"5a77741ced62dab7ad5de5644929278d5b7040de38ddb6e7ca897b3b1d734eb2","cross_cats_sorted":["cs.DS","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-04T17:53:28Z","title_canon_sha256":"9ed4768c61802420b0b1782e478487399927569d9eebaa155f21428e3f2a426e"},"schema_version":"1.0","source":{"id":"2008.01722","kind":"arxiv","version":2}},"canonical_sha256":"e114de2d4e51ad55a130dbd35dc4d5ce616092a822f30a955b6868af66f2a7d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e114de2d4e51ad55a130dbd35dc4d5ce616092a822f30a955b6868af66f2a7d5","first_computed_at":"2026-07-05T03:28:34.955154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:28:34.955154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w64uEOOPwCOuaq0oMjkH0vWJ/NoTwlcadZb4LqYHLny0M+hR+JB3Be23liRqxOjLh6T6mGuoV3iJ1t6tAWjrDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:28:34.955586Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.01722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed40a2260d43c4565a70f4c5f6bdc02da584084544de9f9b617b7a077b9d5d67","sha256:47412a42c4555faccdbdf000322f3e961d11a50100fb5422610c2dbba863b2d8"],"state_sha256":"46dd43336aeee2566ca3cb79e1266f9cd5575dffd81289ba39c538225ba83b4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQy1Ot/aCNOvbfk0mf2OIexy5EZ+e4wBL1iNO7pvqRd7Y/NZRcPLysH4W8BLvfMasjvr3uKDtBGqatuvbXHiBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:16:04.899038Z","bundle_sha256":"74299b0877903d44b9d134db6b8833bcbfcdf4717be318923094c4de885799f2"}}