{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R5M2IP4L2DBXG3KJYK2EYV57QU","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":"e3e7271b13ee14ca6847594059f4ec258c2961c9e17149b7cc1e14fa7e87652b","cross_cats_sorted":["stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-22T18:03:43Z","title_canon_sha256":"6c7da2aa6fc4b1968eb020ba7117f735148a6104bbda121e3f5c82a34f32640d"},"schema_version":"1.0","source":{"id":"1301.5259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5259","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5259v1","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5259","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"R5M2IP4L2DBX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R5M2IP4L2DBXG3KJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R5M2IP4L","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e8e2c9db7ee1d3e7ba8b90f8d0678eca9728599f21b337ceb39e1562911d64b5","target":"graph","created_at":"2026-05-18T03:35:52Z","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":"We will use the factors obtained by correspondence analysis to find biclustering of a contingency table such that the row-column cluster pairs are regular, i.e., they have small discrepancy. In our main theorem, the constant of the so-called volume-regularity is related to the SVD of the normalized contingency table. Our result is applicable to two-way cuts when both the rows and columns are divided into the same number of clusters, thus extending partly the result of Butler estimating the discrepancy of a contingency table by the second largest singular value of the normalized table (one-clus","authors_text":"Marianna Bolla","cross_cats":["stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-22T18:03:43Z","title":"SVD, discrepancy, and regular structure of contingency tables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5259","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:d964474d7d6b23e2ed0336f3c31bb1add57f8bb508ff47fff419801dea97eb9d","target":"record","created_at":"2026-05-18T03:35:52Z","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":"e3e7271b13ee14ca6847594059f4ec258c2961c9e17149b7cc1e14fa7e87652b","cross_cats_sorted":["stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-22T18:03:43Z","title_canon_sha256":"6c7da2aa6fc4b1968eb020ba7117f735148a6104bbda121e3f5c82a34f32640d"},"schema_version":"1.0","source":{"id":"1301.5259","kind":"arxiv","version":1}},"canonical_sha256":"8f59a43f8bd0c3736d49c2b44c57bf85159fe1e32f0d6bc78a202293a3033cc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f59a43f8bd0c3736d49c2b44c57bf85159fe1e32f0d6bc78a202293a3033cc9","first_computed_at":"2026-05-18T03:35:52.459146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.459146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhM16N7svn5axYHpFb5rdoyr43msZ5hOh16TJ0k1M3RFui/48Q3IVuJQOHntJdnosYQTQJfLuXS7jwXPWPKQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.459862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d964474d7d6b23e2ed0336f3c31bb1add57f8bb508ff47fff419801dea97eb9d","sha256:e8e2c9db7ee1d3e7ba8b90f8d0678eca9728599f21b337ceb39e1562911d64b5"],"state_sha256":"914dd19f18b9119c3803b31f411c535de3469a0e5f8bd61b45e96df37beb71fd"}