{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:T566FYOLBGEYA6UIW7T3AFYHH6","short_pith_number":"pith:T566FYOL","canonical_record":{"source":{"id":"1403.5901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-24T10:29:10Z","cross_cats_sorted":[],"title_canon_sha256":"bd1feb52d2b25a4546c5c5902be8c1a81315451f7fee32357bd907bef069efcf","abstract_canon_sha256":"b217a0c7febfa473d106de501d33c574d2add376743730ce3f1564923a109434"},"schema_version":"1.0"},"canonical_sha256":"9f7de2e1cb0989807a88b7e7b017073fbe19cf31cc896cac5b5eb7c2e4731bdf","source":{"kind":"arxiv","id":"1403.5901","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5901","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5901v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5901","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"T566FYOLBGEY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T566FYOLBGEYA6UI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T566FYOL","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:T566FYOLBGEYA6UIW7T3AFYHH6","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-24T10:29:10Z","cross_cats_sorted":[],"title_canon_sha256":"bd1feb52d2b25a4546c5c5902be8c1a81315451f7fee32357bd907bef069efcf","abstract_canon_sha256":"b217a0c7febfa473d106de501d33c574d2add376743730ce3f1564923a109434"},"schema_version":"1.0"},"canonical_sha256":"9f7de2e1cb0989807a88b7e7b017073fbe19cf31cc896cac5b5eb7c2e4731bdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.681760Z","signature_b64":"dZDra1iVVLiJ40fkvJLmg2MMw4K7WamSTvaKVMYN5nF6L42W9TOVUfmih67YCfTNayLAkM3VDLXXu1ldNEVRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f7de2e1cb0989807a88b7e7b017073fbe19cf31cc896cac5b5eb7c2e4731bdf","last_reissued_at":"2026-05-18T01:25:47.681007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.681007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5901","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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NevGIcpbvkF6en89htcDRoCBdb9vhuIU0Jrbvvw3XK1FJJnje1lQeHxhI+QYsM3jePaXYQlMmvXVcVCHTAkxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:40:11.307241Z"},"content_sha256":"d8686ccb82a4a949f502daba019b3e0f5df4a12f69fbdf34d4d4a8619af7bedb","schema_version":"1.0","event_id":"sha256:d8686ccb82a4a949f502daba019b3e0f5df4a12f69fbdf34d4d4a8619af7bedb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:T566FYOLBGEYA6UIW7T3AFYHH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding the largest low-rank clusters with Ky Fan $2$-$k$-norm and $\\ell_1$-norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Stephen Vavasis, Xuan Vinh Doan","submitted_at":"2014-03-24T10:29:10Z","abstract_excerpt":"We propose a convex optimization formulation with the Ky Fan $2$-$k$-norm and $\\ell_1$-norm to find $k$ largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under certain hypotheses, with high probability, the approach can recover rank-one submatrix blocks even when they are corrupted with random noise and inserted into a much larger matrix with other random noise blocks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5901","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":""},"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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjqgX1R/qmjJZ0zvf5q1OlXF0+KBulAY8BSfff5gn1uXaJU/ZLA4MFM468cqeZlCkKKzyEbjNlx/Dcm/CELGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:40:11.307605Z"},"content_sha256":"5f24dc2d8c57f0a2d324b2286898086f528f0ec853ee67d1acd0dfa708350b30","schema_version":"1.0","event_id":"sha256:5f24dc2d8c57f0a2d324b2286898086f528f0ec853ee67d1acd0dfa708350b30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T566FYOLBGEYA6UIW7T3AFYHH6/bundle.json","state_url":"https://pith.science/pith/T566FYOLBGEYA6UIW7T3AFYHH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T566FYOLBGEYA6UIW7T3AFYHH6/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":"2026-06-04T01:40:11Z","links":{"resolver":"https://pith.science/pith/T566FYOLBGEYA6UIW7T3AFYHH6","bundle":"https://pith.science/pith/T566FYOLBGEYA6UIW7T3AFYHH6/bundle.json","state":"https://pith.science/pith/T566FYOLBGEYA6UIW7T3AFYHH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T566FYOLBGEYA6UIW7T3AFYHH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T566FYOLBGEYA6UIW7T3AFYHH6","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":"b217a0c7febfa473d106de501d33c574d2add376743730ce3f1564923a109434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-24T10:29:10Z","title_canon_sha256":"bd1feb52d2b25a4546c5c5902be8c1a81315451f7fee32357bd907bef069efcf"},"schema_version":"1.0","source":{"id":"1403.5901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5901","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5901v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5901","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"T566FYOLBGEY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T566FYOLBGEYA6UI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T566FYOL","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:5f24dc2d8c57f0a2d324b2286898086f528f0ec853ee67d1acd0dfa708350b30","target":"graph","created_at":"2026-05-18T01:25:47Z","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 propose a convex optimization formulation with the Ky Fan $2$-$k$-norm and $\\ell_1$-norm to find $k$ largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under certain hypotheses, with high probability, the approach can recover rank-one submatrix blocks even when they are corrupted with random noise and inserted into a much larger matrix with other random noise blocks.","authors_text":"Stephen Vavasis, Xuan Vinh Doan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-24T10:29:10Z","title":"Finding the largest low-rank clusters with Ky Fan $2$-$k$-norm and $\\ell_1$-norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5901","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:d8686ccb82a4a949f502daba019b3e0f5df4a12f69fbdf34d4d4a8619af7bedb","target":"record","created_at":"2026-05-18T01:25:47Z","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":"b217a0c7febfa473d106de501d33c574d2add376743730ce3f1564923a109434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-24T10:29:10Z","title_canon_sha256":"bd1feb52d2b25a4546c5c5902be8c1a81315451f7fee32357bd907bef069efcf"},"schema_version":"1.0","source":{"id":"1403.5901","kind":"arxiv","version":2}},"canonical_sha256":"9f7de2e1cb0989807a88b7e7b017073fbe19cf31cc896cac5b5eb7c2e4731bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f7de2e1cb0989807a88b7e7b017073fbe19cf31cc896cac5b5eb7c2e4731bdf","first_computed_at":"2026-05-18T01:25:47.681007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:47.681007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZDra1iVVLiJ40fkvJLmg2MMw4K7WamSTvaKVMYN5nF6L42W9TOVUfmih67YCfTNayLAkM3VDLXXu1ldNEVRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:47.681760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8686ccb82a4a949f502daba019b3e0f5df4a12f69fbdf34d4d4a8619af7bedb","sha256:5f24dc2d8c57f0a2d324b2286898086f528f0ec853ee67d1acd0dfa708350b30"],"state_sha256":"8f0202809785e23e2337ce5947d656688db27ecf5d9e437b15e9154dd640adb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZNZHE1m0Ziz/JE7VqpcvQ3vhpTJGWtEHC5TSSHUf1fBZmKLEoGLUMPrnuzlC3Xn57Sny/7O0mAPSNKBTQ+3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:40:11.309682Z","bundle_sha256":"11da08a73374360018babc7fd973e8a04ef3ed275640452200a4e573cd793b43"}}