{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IAROY3QVFW6D76YUIW7S6U2J4I","short_pith_number":"pith:IAROY3QV","canonical_record":{"source":{"id":"1310.0154","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-01T06:37:18Z","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"title_canon_sha256":"4670dc6e2a46ea7701b495e4f2de92ede97f87107507e63e1a3de8f3e50fae57","abstract_canon_sha256":"78820c5f60d1e85a40b313091cfc1fe0bafd2cf94e695c70af70a882c8258c0a"},"schema_version":"1.0"},"canonical_sha256":"4022ec6e152dbc3ffb1445bf2f5349e221595e36b4386a946aa9d092602c3c20","source":{"kind":"arxiv","id":"1310.0154","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0154","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0154v4","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0154","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"IAROY3QVFW6D","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IAROY3QVFW6D76YU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IAROY3QV","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IAROY3QVFW6D76YUIW7S6U2J4I","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0154","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-01T06:37:18Z","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"title_canon_sha256":"4670dc6e2a46ea7701b495e4f2de92ede97f87107507e63e1a3de8f3e50fae57","abstract_canon_sha256":"78820c5f60d1e85a40b313091cfc1fe0bafd2cf94e695c70af70a882c8258c0a"},"schema_version":"1.0"},"canonical_sha256":"4022ec6e152dbc3ffb1445bf2f5349e221595e36b4386a946aa9d092602c3c20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:03.728354Z","signature_b64":"xLJ3U5SS9pK9zE6hNXHE2m1HeJb/1VDcAWIsqE82VsruMbk8GxiwTYaAwY4GPmbuLkgpoqURZHqEr+xJDswxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4022ec6e152dbc3ffb1445bf2f5349e221595e36b4386a946aa9d092602c3c20","last_reissued_at":"2026-05-18T00:59:03.727535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:03.727535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0154","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gys4mf3GpeTJ6OayN3TlYYB4RcCiiTf6pzWHavTRReqNjSbfdmJIFNrK1ULuItrDYAIazOybYNGXpbsYpWqsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:58:14.622702Z"},"content_sha256":"54f04f07a8df3a0cb92ff14737748c0315e1bff0276425931ed11a5f07da8985","schema_version":"1.0","event_id":"sha256:54f04f07a8df3a0cb92ff14737748c0315e1bff0276425931ed11a5f07da8985"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IAROY3QVFW6D76YUIW7S6U2J4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incoherence-Optimal Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Yudong Chen","submitted_at":"2013-10-01T06:37:18Z","abstract_excerpt":"This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is order-wise optimal with respect to the incoherence parameter (as well as to the rank $r$ and the matrix dimension $n$ up to a log factor). As a consequence, we improve the sample complexity of recovering a semidefinite matrix from $O(nr^{2}\\log^{2}n)$ to $O(nr\\log^{2}n)$, and the highest allowable rank from $\\Theta(\\sqrt{n}/\\log n)$ to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0154","kind":"arxiv","version":4},"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":"2026-05-18T00:59:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNd2x33DHcKn42wxtk8Ty5HifaV3l98SjJsAxKTyCXHfXt2twva6I9CO4vjqq7f6iRMWLLppr7m/OkRgbAT/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:58:14.623374Z"},"content_sha256":"7273e72c7f95029aad9ee0d8eabbde64c1d6e6d686a58575b82934c0b1171aab","schema_version":"1.0","event_id":"sha256:7273e72c7f95029aad9ee0d8eabbde64c1d6e6d686a58575b82934c0b1171aab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IAROY3QVFW6D76YUIW7S6U2J4I/bundle.json","state_url":"https://pith.science/pith/IAROY3QVFW6D76YUIW7S6U2J4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IAROY3QVFW6D76YUIW7S6U2J4I/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":"2026-05-26T03:58:14Z","links":{"resolver":"https://pith.science/pith/IAROY3QVFW6D76YUIW7S6U2J4I","bundle":"https://pith.science/pith/IAROY3QVFW6D76YUIW7S6U2J4I/bundle.json","state":"https://pith.science/pith/IAROY3QVFW6D76YUIW7S6U2J4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IAROY3QVFW6D76YUIW7S6U2J4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IAROY3QVFW6D76YUIW7S6U2J4I","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":"78820c5f60d1e85a40b313091cfc1fe0bafd2cf94e695c70af70a882c8258c0a","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-01T06:37:18Z","title_canon_sha256":"4670dc6e2a46ea7701b495e4f2de92ede97f87107507e63e1a3de8f3e50fae57"},"schema_version":"1.0","source":{"id":"1310.0154","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0154","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0154v4","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0154","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"IAROY3QVFW6D","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IAROY3QVFW6D76YU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IAROY3QV","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:7273e72c7f95029aad9ee0d8eabbde64c1d6e6d686a58575b82934c0b1171aab","target":"graph","created_at":"2026-05-18T00:59:03Z","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":"This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is order-wise optimal with respect to the incoherence parameter (as well as to the rank $r$ and the matrix dimension $n$ up to a log factor). As a consequence, we improve the sample complexity of recovering a semidefinite matrix from $O(nr^{2}\\log^{2}n)$ to $O(nr\\log^{2}n)$, and the highest allowable rank from $\\Theta(\\sqrt{n}/\\log n)$ to $","authors_text":"Yudong Chen","cross_cats":["cs.LG","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-01T06:37:18Z","title":"Incoherence-Optimal Matrix Completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0154","kind":"arxiv","version":4},"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":"sha256:54f04f07a8df3a0cb92ff14737748c0315e1bff0276425931ed11a5f07da8985","target":"record","created_at":"2026-05-18T00:59:03Z","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":"78820c5f60d1e85a40b313091cfc1fe0bafd2cf94e695c70af70a882c8258c0a","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-01T06:37:18Z","title_canon_sha256":"4670dc6e2a46ea7701b495e4f2de92ede97f87107507e63e1a3de8f3e50fae57"},"schema_version":"1.0","source":{"id":"1310.0154","kind":"arxiv","version":4}},"canonical_sha256":"4022ec6e152dbc3ffb1445bf2f5349e221595e36b4386a946aa9d092602c3c20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4022ec6e152dbc3ffb1445bf2f5349e221595e36b4386a946aa9d092602c3c20","first_computed_at":"2026-05-18T00:59:03.727535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:03.727535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xLJ3U5SS9pK9zE6hNXHE2m1HeJb/1VDcAWIsqE82VsruMbk8GxiwTYaAwY4GPmbuLkgpoqURZHqEr+xJDswxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:03.728354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0154","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54f04f07a8df3a0cb92ff14737748c0315e1bff0276425931ed11a5f07da8985","sha256:7273e72c7f95029aad9ee0d8eabbde64c1d6e6d686a58575b82934c0b1171aab"],"state_sha256":"6fd127ef4fa63ae29a45f8762a75f30d04d7f38813580181d9cd7890538ba82d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BQYcBx3tdpHHk07nUCXZBSH9REgo5PMf8cJNziyLPQj8BlvJeVhxEjFTn6Nb4ld576G5zIlbHXcQ432f7K8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:58:14.627296Z","bundle_sha256":"294fc8b7866c09942c7e6befba226a6b8372a716895d7eb41c90f30a7e8515f0"}}