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The radius of the largest inscribed ball is closely related to the existence of integer points in the polytope. We show that for m=2^O(sqrt{n}), there exist constants c_0 < c_1 such that with high probability, random polytopes are integer feasible if the radius of the largest ball contained in the polytope is at least c_1sqrt{log(m/n)}; and integer infeasible if th"},"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":"1111.4649","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-20T16:53:55Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d44d10ae31449ce526d55f4948a7e3f8c5b19d41e2b984499c96765853b24d7d","abstract_canon_sha256":"3918216a029c37aff51a2835cc8f99754cd0bed3ee18c5f89312a930e2d455bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:07.683711Z","signature_b64":"6LXPiEsS6U644OrfzpU9nuBsYJ3W1p45t2Ozi2kSs7cX4Z+jaSbQpumUS9iBWeX3WXyfYi3lva3V+AVAPKaUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdc15355b43acfa606b6cbf8c3f701343676abb47141e6049635dc6d46768530","last_reissued_at":"2026-05-18T03:15:07.683002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:07.683002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer Feasibility of Random Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Karthekeyan Chandrasekaran, Santosh Vempala","submitted_at":"2011-11-20T16:53:55Z","abstract_excerpt":"We study integer programming instances over polytopes P(A,b)={x:Ax<=b} where the constraint matrix A is random, i.e., its entries are i.i.d. 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We show that for m=2^O(sqrt{n}), there exist constants c_0 < c_1 such that with high probability, random polytopes are integer feasible if the radius of the largest ball contained in the polytope is at least c_1sqrt{log(m/n)}; and integer infeasible if th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4649","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.4649","created_at":"2026-05-18T03:15:07.683098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.4649v3","created_at":"2026-05-18T03:15:07.683098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4649","created_at":"2026-05-18T03:15:07.683098+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZXAVGVNUHLH2","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZXAVGVNUHLH2MBVW","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZXAVGVNU","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ","json":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ.json","graph_json":"https://pith.science/api/pith-number/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/graph.json","events_json":"https://pith.science/api/pith-number/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/events.json","paper":"https://pith.science/paper/ZXAVGVNU"},"agent_actions":{"view_html":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ","download_json":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ.json","view_paper":"https://pith.science/paper/ZXAVGVNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.4649&json=true","fetch_graph":"https://pith.science/api/pith-number/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/action/storage_attestation","attest_author":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/action/author_attestation","sign_citation":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/action/citation_signature","submit_replication":"https://pith.science/pith/ZXAVGVNUHLH2MBVWZP4MH5YBGQ/action/replication_record"}},"created_at":"2026-05-18T03:15:07.683098+00:00","updated_at":"2026-05-18T03:15:07.683098+00:00"}