{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X7ZWWCBMALP7IXLE44P6TBOBAY","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":"8e0389b9e879c72fda6e7aa2eaefbc71f0ec5c64a4d5f14ce0a90f4a5bd49ec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-21T17:22:13Z","title_canon_sha256":"606a4c19f3791e9816ef9f900b7f346884be763d9255a2c0f7b470f9602eaabe"},"schema_version":"1.0","source":{"id":"1305.4891","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4891","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4891v2","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4891","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"X7ZWWCBMALP7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X7ZWWCBMALP7IXLE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X7ZWWCBM","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:1519df0aa5c9394f90107114eb5684efe959982d93b08bf7e6488de7a01cd360","target":"graph","created_at":"2026-05-18T02:07:32Z","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 consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original combinatorial problem is NP-hard, we show that the densest k-subgraph can be recovered from the solution of our convex relaxation for certain program inputs. In particular, we establish exact recovery in the case that the input graph contains a single planted clique plus noise in the form of corrupted adjacency relationships. We consider two constructions for th","authors_text":"Brendan P.W. Ames","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-21T17:22:13Z","title":"Guaranteed Recovery of Planted Cliques and Dense Subgraphs by Convex Relaxation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4891","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:baa0035110828dd813049d4924cacbf17afd982bafd4dee3e6f212f477e10e88","target":"record","created_at":"2026-05-18T02:07:32Z","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":"8e0389b9e879c72fda6e7aa2eaefbc71f0ec5c64a4d5f14ce0a90f4a5bd49ec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-21T17:22:13Z","title_canon_sha256":"606a4c19f3791e9816ef9f900b7f346884be763d9255a2c0f7b470f9602eaabe"},"schema_version":"1.0","source":{"id":"1305.4891","kind":"arxiv","version":2}},"canonical_sha256":"bff36b082c02dff45d64e71fe985c106382153a575911eda5a7a25ca4d6a6435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bff36b082c02dff45d64e71fe985c106382153a575911eda5a7a25ca4d6a6435","first_computed_at":"2026-05-18T02:07:32.219643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.219643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sbVSiB2ikfBu7BjPC8swvQ/nzgT9GLsJFsWX+yhy0jlq0puKFMZ9pA1EYRDvSl2xnrtqaY4TWapiNDAxQO+7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.220264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4891","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa0035110828dd813049d4924cacbf17afd982bafd4dee3e6f212f477e10e88","sha256:1519df0aa5c9394f90107114eb5684efe959982d93b08bf7e6488de7a01cd360"],"state_sha256":"416a5f53ff2edda1b78cdae41c88d4f88ea612c02246b24d28a44c484591e762"}