{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A7IKYXIEKOSEIDR6TJWDU76ZAJ","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":"07be77145b33a2208dc0c0f00de4a77fa6295b34b35c73572a1a19e061070558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-06-14T08:20:39Z","title_canon_sha256":"bc29b3ad97530361f4d23e6ede0ccb43457fa64f367edf2947d34b9da23a4a98"},"schema_version":"1.0","source":{"id":"1406.3700","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3700","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3700v3","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3700","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"A7IKYXIEKOSE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A7IKYXIEKOSEIDR6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A7IKYXIE","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:649721b9518aee239de44db9e4bfd4cf04072c2d85926ca9bf5e3640ba62660a","target":"graph","created_at":"2026-05-17T23:43:54Z","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":"Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide an fpt-reduction from $k$-clique to $k$-biclique, thus solving this longstanding open problem.\n  Our reduction use a class of bipartite graphs with a threshold property of independent interest. More specifically, for positive integers $n$, $s$ and $t$, we consider a bipartite graph $G=(A\\;\\dot\\cup\\;B, E)$ such that $A$ can be partitioned into $A=V_1\\;\\dot\\cu","authors_text":"Bingkai Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-06-14T08:20:39Z","title":"The Parameterized Complexity of k-Biclique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3700","kind":"arxiv","version":3},"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":"sha256:866a386bc7d1017b8a47640d704a825f51884ec3e63db7c7df5ae981a188769c","target":"record","created_at":"2026-05-17T23:43:54Z","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":"07be77145b33a2208dc0c0f00de4a77fa6295b34b35c73572a1a19e061070558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-06-14T08:20:39Z","title_canon_sha256":"bc29b3ad97530361f4d23e6ede0ccb43457fa64f367edf2947d34b9da23a4a98"},"schema_version":"1.0","source":{"id":"1406.3700","kind":"arxiv","version":3}},"canonical_sha256":"07d0ac5d0453a4440e3e9a6c3a7fd902410448bc6654ffeaca55dec58ff391ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07d0ac5d0453a4440e3e9a6c3a7fd902410448bc6654ffeaca55dec58ff391ce","first_computed_at":"2026-05-17T23:43:54.488286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:54.488286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2k1fQXibgpR9BvWfkEp+TTEea9euuWkNAJuZoWoWoHEtRY1AzLx/xZnabaNSrSzzcHqdZsiIET3jSg2BomADw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:54.488995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3700","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:866a386bc7d1017b8a47640d704a825f51884ec3e63db7c7df5ae981a188769c","sha256:649721b9518aee239de44db9e4bfd4cf04072c2d85926ca9bf5e3640ba62660a"],"state_sha256":"106362a123c365c322f504983a889eee7cc31e9d1bf461e64edf95c350d4269e"}