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In other words, every polyhedron Q that can be linearly projected on conv(X) must have exponentially many facets.\n  In fact, the same result also applies if conv(X) is restricted to be a matroid polytope.\n  Conditioning on NP not contained in P_{/poly}, our result rules out the existence of any compact formulation for the TSP polytope, even if the formulation "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.0036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-30T00:41:13Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"ef8417678fe9925337a45b1969a5f5bafd29f75c8b869824f03817523717a324","abstract_canon_sha256":"005ce46f688b20675946b531fff1427887f1539ee51466dcf5d03f75f66e396e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:12.629542Z","signature_b64":"80IDewtdOCpaN9vtEsUc3VN58hUxz6yCDwwJLjt3QXVkKogGJCggh/GQkHSRB9VHjl1F4DiHqcJ8c5Kl33zHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f75f5c7001d5b622ed1ac6d43722b98ebcf520eb5b5ced11357913ae13791816","last_reissued_at":"2026-05-18T04:23:12.628884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:12.628884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some 0/1 polytopes need exponential size extended formulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Thomas Rothvo{\\ss}","submitted_at":"2011-04-30T00:41:13Z","abstract_excerpt":"We prove that there are 0/1 polytopes P that do not admit a compact LP formulation. 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