{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:SU2WRSUEUUYVNCHOK6EKMCUS3V","short_pith_number":"pith:SU2WRSUE","canonical_record":{"source":{"id":"2105.11004","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-23T19:21:55Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"title_canon_sha256":"74a0f8444fcc31c254f00a6ae85847e13588f39ebe92959a9283a7665b006bd4","abstract_canon_sha256":"8563322892c99d9bfdfd024aa2ac4ff4070fb27df4112f4880757d069578eccd"},"schema_version":"1.0"},"canonical_sha256":"953568ca84a5315688ee5788a60a92dd71954960853bbf3ad775f6050d9b43c8","source":{"kind":"arxiv","id":"2105.11004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11004","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11004v1","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11004","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_12","alias_value":"SU2WRSUEUUYV","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_16","alias_value":"SU2WRSUEUUYVNCHO","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_8","alias_value":"SU2WRSUE","created_at":"2026-07-05T04:02:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:SU2WRSUEUUYVNCHOK6EKMCUS3V","target":"record","payload":{"canonical_record":{"source":{"id":"2105.11004","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-23T19:21:55Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"title_canon_sha256":"74a0f8444fcc31c254f00a6ae85847e13588f39ebe92959a9283a7665b006bd4","abstract_canon_sha256":"8563322892c99d9bfdfd024aa2ac4ff4070fb27df4112f4880757d069578eccd"},"schema_version":"1.0"},"canonical_sha256":"953568ca84a5315688ee5788a60a92dd71954960853bbf3ad775f6050d9b43c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:02:16.562984Z","signature_b64":"uPlfRhd+Dx3bzGzI/IyUwFOxSFh5m8uZ2hwACySvAaa6Fh24OKTD4/ZPYJ9ycgEqHJ/59YL4bqjP2AvcgsPCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"953568ca84a5315688ee5788a60a92dd71954960853bbf3ad775f6050d9b43c8","last_reissued_at":"2026-07-05T04:02:16.562491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:02:16.562491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.11004","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":"2026-07-05T04:02:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gh1Oa4SYIpNzi/fNRPI+PtfG+w3/k/oK7Ekc/8tsIcCUznVEXMfkXukmD5aEuoh6vnwaXahgsQ/xD5iJALAiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:55:49.121014Z"},"content_sha256":"3139eae4bdf6f3da77cb68f9a79404069659a606081b62ddbbfd62d69c6a0fd4","schema_version":"1.0","event_id":"sha256:3139eae4bdf6f3da77cb68f9a79404069659a606081b62ddbbfd62d69c6a0fd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:SU2WRSUEUUYVNCHOK6EKMCUS3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating leverage scores via rank revealing methods and randomization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"primary_cat":"cs.DS","authors_text":"Aleksandros Sobczyk (1), Efstratios Gallopoulos (2) ((1) IBM Research Europe, Greece), Informatics Department, Switzerland (2) Computer Engineering, University of Patras, Zurich","submitted_at":"2021-05-23T19:21:55Z","abstract_excerpt":"We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction transforms. We first develop a set of fast novel algorithms for rank estimation, column subset selection and least squares preconditioning. We then describe the design and implementation of leverage score estimators based on these primitives. These estimators are also effective for rank deficient input, which is frequently the case in data "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11004","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/2105.11004/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":"2026-07-05T04:02:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G70HuiZF6vnxCTQ2NGxvZi03Iag26qnumo9s8WL73ee5GyYEF0MLl85fe49piketXco9HyX7VRGE8S526EDZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:55:49.121522Z"},"content_sha256":"c9572da49ac69401a3ab6459c7a7ef730e8dbe4fa6633b6f014999c095c4a2d0","schema_version":"1.0","event_id":"sha256:c9572da49ac69401a3ab6459c7a7ef730e8dbe4fa6633b6f014999c095c4a2d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/bundle.json","state_url":"https://pith.science/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/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":"2026-08-09T05:55:49Z","links":{"resolver":"https://pith.science/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V","bundle":"https://pith.science/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/bundle.json","state":"https://pith.science/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SU2WRSUEUUYVNCHOK6EKMCUS3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SU2WRSUEUUYVNCHOK6EKMCUS3V","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":"8563322892c99d9bfdfd024aa2ac4ff4070fb27df4112f4880757d069578eccd","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-23T19:21:55Z","title_canon_sha256":"74a0f8444fcc31c254f00a6ae85847e13588f39ebe92959a9283a7665b006bd4"},"schema_version":"1.0","source":{"id":"2105.11004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11004","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11004v1","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11004","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_12","alias_value":"SU2WRSUEUUYV","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_16","alias_value":"SU2WRSUEUUYVNCHO","created_at":"2026-07-05T04:02:16Z"},{"alias_kind":"pith_short_8","alias_value":"SU2WRSUE","created_at":"2026-07-05T04:02:16Z"}],"graph_snapshots":[{"event_id":"sha256:c9572da49ac69401a3ab6459c7a7ef730e8dbe4fa6633b6f014999c095c4a2d0","target":"graph","created_at":"2026-07-05T04:02:16Z","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/2105.11004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction transforms. We first develop a set of fast novel algorithms for rank estimation, column subset selection and least squares preconditioning. We then describe the design and implementation of leverage score estimators based on these primitives. These estimators are also effective for rank deficient input, which is frequently the case in data ","authors_text":"Aleksandros Sobczyk (1), Efstratios Gallopoulos (2) ((1) IBM Research Europe, Greece), Informatics Department, Switzerland (2) Computer Engineering, University of Patras, Zurich","cross_cats":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-23T19:21:55Z","title":"Estimating leverage scores via rank revealing methods and randomization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11004","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":"sha256:3139eae4bdf6f3da77cb68f9a79404069659a606081b62ddbbfd62d69c6a0fd4","target":"record","created_at":"2026-07-05T04:02:16Z","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":"8563322892c99d9bfdfd024aa2ac4ff4070fb27df4112f4880757d069578eccd","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-23T19:21:55Z","title_canon_sha256":"74a0f8444fcc31c254f00a6ae85847e13588f39ebe92959a9283a7665b006bd4"},"schema_version":"1.0","source":{"id":"2105.11004","kind":"arxiv","version":1}},"canonical_sha256":"953568ca84a5315688ee5788a60a92dd71954960853bbf3ad775f6050d9b43c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"953568ca84a5315688ee5788a60a92dd71954960853bbf3ad775f6050d9b43c8","first_computed_at":"2026-07-05T04:02:16.562491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:02:16.562491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uPlfRhd+Dx3bzGzI/IyUwFOxSFh5m8uZ2hwACySvAaa6Fh24OKTD4/ZPYJ9ycgEqHJ/59YL4bqjP2AvcgsPCAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:02:16.562984Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.11004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3139eae4bdf6f3da77cb68f9a79404069659a606081b62ddbbfd62d69c6a0fd4","sha256:c9572da49ac69401a3ab6459c7a7ef730e8dbe4fa6633b6f014999c095c4a2d0"],"state_sha256":"60388d6e025b6b97710294db718a3b555cab23556032a1b1c39dd66207ab3bd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5CiG+v10OovOp6Bky1Suc03yQQbDrodQ7JWO8+eiTirgoyo4kjyCikZo9pbkqg3L8dSrpRHJu7zCouQdcNCYCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T05:55:49.125161Z","bundle_sha256":"88fa5fac2553baadbb02e5048ecf2bc183142143ecb12ffdbc90bf5bb43a37dc"}}