{"paper":{"title":"Team Diagonalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Holger Spakowski, Lane A. Hemaspaandra","submitted_at":"2018-07-28T23:30:29Z","abstract_excerpt":"Ten years ago, Gla{\\ss}er, Pavan, Selman, and Zhang [GPSZ08] proved that if P $\\neq$ NP, then all NP-complete sets can be simply split into two NP-complete sets.\n  That advance might naturally make one wonder about a quite different potential consequence of NP-completeness: Can the union of easy NP sets ever be hard? In particular, can the union of two non-NP-complete NP sets ever be NP-complete?\n  Amazingly, Ladner [Lad75] resolved this more than forty years ago: If P $\\neq$ NP, then all NP-complete sets can be simply split into two non-NP-complete NP sets. Indeed, this holds even when one re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10983","kind":"arxiv","version":1},"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"}