{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OKSGOKT6BCOQUSGTX5JMYLNY3L","short_pith_number":"pith:OKSGOKT6","canonical_record":{"source":{"id":"2407.01698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-07-01T18:10:19Z","cross_cats_sorted":["cs.NA","stat.ML"],"title_canon_sha256":"0de52f011919df607b34530480df87127c4207eb5f4d00252fcce29147288305","abstract_canon_sha256":"dfdc5978cae14b45735330121488dd7684c1c4b25d1a4624ffdf2a77fad28be7"},"schema_version":"1.0"},"canonical_sha256":"72a4672a7e089d0a48d3bf52cc2db8dae37caf8886faaf7fbbc40894b201e045","source":{"kind":"arxiv","id":"2407.01698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01698","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01698v2","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01698","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_12","alias_value":"OKSGOKT6BCOQ","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_16","alias_value":"OKSGOKT6BCOQUSGT","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_8","alias_value":"OKSGOKT6","created_at":"2026-07-05T08:53:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OKSGOKT6BCOQUSGTX5JMYLNY3L","target":"record","payload":{"canonical_record":{"source":{"id":"2407.01698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-07-01T18:10:19Z","cross_cats_sorted":["cs.NA","stat.ML"],"title_canon_sha256":"0de52f011919df607b34530480df87127c4207eb5f4d00252fcce29147288305","abstract_canon_sha256":"dfdc5978cae14b45735330121488dd7684c1c4b25d1a4624ffdf2a77fad28be7"},"schema_version":"1.0"},"canonical_sha256":"72a4672a7e089d0a48d3bf52cc2db8dae37caf8886faaf7fbbc40894b201e045","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:53:23.720286Z","signature_b64":"Ywcl8FTYvueVmvgqjsbGqqV6Y+X0wTUMnwr1uEiGP2lR/LdL0wLH+0ZiOUJsI/oyKpo0VB7MjPpi/3nDuSdzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72a4672a7e089d0a48d3bf52cc2db8dae37caf8886faaf7fbbc40894b201e045","last_reissued_at":"2026-07-05T08:53:23.719871Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:53:23.719871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.01698","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":"2026-07-05T08:53:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+L9eLrRf4aNJbzxHILwWZqTMg4ZC5GQTiuS6BY0H158CkkWNVaUJa19bpnlaF93XPYS6aoJZwgKaqiHd/ceYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:35:06.522176Z"},"content_sha256":"711a5314d08896497b90a7019feec4dfb17240e93c6d2b380d8bddb13d1ee6dd","schema_version":"1.0","event_id":"sha256:711a5314d08896497b90a7019feec4dfb17240e93c6d2b380d8bddb13d1ee6dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OKSGOKT6BCOQUSGTX5JMYLNY3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Column and row subset selection using nuclear scores: algorithms and theory for Nystr\\\"{o}m approximation, CUR decomposition, and graph Laplacian reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Mark Fornace, Michael Lindsey","submitted_at":"2024-07-01T18:10:19Z","abstract_excerpt":"Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified methodologies for fast, efficient, and theoretically guaranteed column selection. First we derive and implement a sparsity-exploiting deterministic algorithm applicable to tasks including kernel approximation and CUR decomposition. Next, we develop a matrix-free formalism relying on a randomization scheme satisfying guaranteed concentration bounds, applying th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01698","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/2407.01698/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":"2026-07-05T08:53:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0fSuSey5wbt1yExYWWKImVS8l+/FWCC0IZD8o+hbgPah4iv/KSUnNNwAfYbvNGtXqI3m9Dgdd9FL/+P8fTxZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:35:06.522760Z"},"content_sha256":"df103c72dd2fcaac393fe6742c43e777057fd523eebb60ae1b9eeb55a58c2d3c","schema_version":"1.0","event_id":"sha256:df103c72dd2fcaac393fe6742c43e777057fd523eebb60ae1b9eeb55a58c2d3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/bundle.json","state_url":"https://pith.science/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/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":"2026-08-15T11:35:06Z","links":{"resolver":"https://pith.science/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L","bundle":"https://pith.science/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/bundle.json","state":"https://pith.science/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OKSGOKT6BCOQUSGTX5JMYLNY3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OKSGOKT6BCOQUSGTX5JMYLNY3L","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":"dfdc5978cae14b45735330121488dd7684c1c4b25d1a4624ffdf2a77fad28be7","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-07-01T18:10:19Z","title_canon_sha256":"0de52f011919df607b34530480df87127c4207eb5f4d00252fcce29147288305"},"schema_version":"1.0","source":{"id":"2407.01698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01698","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01698v2","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01698","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_12","alias_value":"OKSGOKT6BCOQ","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_16","alias_value":"OKSGOKT6BCOQUSGT","created_at":"2026-07-05T08:53:23Z"},{"alias_kind":"pith_short_8","alias_value":"OKSGOKT6","created_at":"2026-07-05T08:53:23Z"}],"graph_snapshots":[{"event_id":"sha256:df103c72dd2fcaac393fe6742c43e777057fd523eebb60ae1b9eeb55a58c2d3c","target":"graph","created_at":"2026-07-05T08:53:23Z","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/2407.01698/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified methodologies for fast, efficient, and theoretically guaranteed column selection. First we derive and implement a sparsity-exploiting deterministic algorithm applicable to tasks including kernel approximation and CUR decomposition. Next, we develop a matrix-free formalism relying on a randomization scheme satisfying guaranteed concentration bounds, applying th","authors_text":"Mark Fornace, Michael Lindsey","cross_cats":["cs.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-07-01T18:10:19Z","title":"Column and row subset selection using nuclear scores: algorithms and theory for Nystr\\\"{o}m approximation, CUR decomposition, and graph Laplacian reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01698","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":"sha256:711a5314d08896497b90a7019feec4dfb17240e93c6d2b380d8bddb13d1ee6dd","target":"record","created_at":"2026-07-05T08:53:23Z","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":"dfdc5978cae14b45735330121488dd7684c1c4b25d1a4624ffdf2a77fad28be7","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-07-01T18:10:19Z","title_canon_sha256":"0de52f011919df607b34530480df87127c4207eb5f4d00252fcce29147288305"},"schema_version":"1.0","source":{"id":"2407.01698","kind":"arxiv","version":2}},"canonical_sha256":"72a4672a7e089d0a48d3bf52cc2db8dae37caf8886faaf7fbbc40894b201e045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72a4672a7e089d0a48d3bf52cc2db8dae37caf8886faaf7fbbc40894b201e045","first_computed_at":"2026-07-05T08:53:23.719871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:53:23.719871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ywcl8FTYvueVmvgqjsbGqqV6Y+X0wTUMnwr1uEiGP2lR/LdL0wLH+0ZiOUJsI/oyKpo0VB7MjPpi/3nDuSdzBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:53:23.720286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.01698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:711a5314d08896497b90a7019feec4dfb17240e93c6d2b380d8bddb13d1ee6dd","sha256:df103c72dd2fcaac393fe6742c43e777057fd523eebb60ae1b9eeb55a58c2d3c"],"state_sha256":"6702bf8460ec75a6db2bf0468a6aa6dcc7c7ad2d71319a99c11518710c663451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAHIasp9lbgDf516AkI4+6jVwnlY/xfwNvi+AFC9YojcEk/a8bpmYGEqRLeEc0hQhJO6KOFRa5fQe+fo2WcZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T11:35:06.526877Z","bundle_sha256":"adc73b601b77d049eddcd2cfe2943e7d1930b124af25934b6aa334f493e72012"}}