{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MZ4HSCHSA6F7YE2OBFDFWSQKKO","short_pith_number":"pith:MZ4HSCHS","schema_version":"1.0","canonical_sha256":"66787908f2078bfc134e09465b4a0a53bde04c0e9dfa03213c0ba14255b3243c","source":{"kind":"arxiv","id":"1002.0562","version":1},"attestation_state":"computed","paper":{"title":"Minimum and maximum against k lies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.GT"],"primary_cat":"cs.DS","authors_text":"Ji\\v{r}\\'i Matou\\v{s}ek, Michael Hoffmann, Philipp Zumstein, Yoshio Okamoto","submitted_at":"2010-02-02T18:54:35Z","abstract_excerpt":"A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The kno"},"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":"1002.0562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-02-02T18:54:35Z","cross_cats_sorted":["cs.CC","cs.GT"],"title_canon_sha256":"9651cea7ec839c6e4440f1b06081aa8ead812f23522a1a1024ac20cd65609d29","abstract_canon_sha256":"af0ab5eb8ef7ab111b85750a76278abe2e1e761939a0f592eb8bf135a3d35e05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:20.766022Z","signature_b64":"5B5J6etQxhidqcuC8K0m9Bbb7ny9scGDeAzLtH5NADzdXQdrnESEqsiHdfyVHNl2xkgPDX2xkUcSWpned6LIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66787908f2078bfc134e09465b4a0a53bde04c0e9dfa03213c0ba14255b3243c","last_reissued_at":"2026-05-18T02:09:20.765556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:20.765556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum and maximum against k lies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.GT"],"primary_cat":"cs.DS","authors_text":"Ji\\v{r}\\'i Matou\\v{s}ek, Michael Hoffmann, Philipp Zumstein, Yoshio Okamoto","submitted_at":"2010-02-02T18:54:35Z","abstract_excerpt":"A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0562","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1002.0562","created_at":"2026-05-18T02:09:20.765627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0562v1","created_at":"2026-05-18T02:09:20.765627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0562","created_at":"2026-05-18T02:09:20.765627+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZ4HSCHSA6F7","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZ4HSCHSA6F7YE2O","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZ4HSCHS","created_at":"2026-05-18T12:26:10.704358+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/MZ4HSCHSA6F7YE2OBFDFWSQKKO","json":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO.json","graph_json":"https://pith.science/api/pith-number/MZ4HSCHSA6F7YE2OBFDFWSQKKO/graph.json","events_json":"https://pith.science/api/pith-number/MZ4HSCHSA6F7YE2OBFDFWSQKKO/events.json","paper":"https://pith.science/paper/MZ4HSCHS"},"agent_actions":{"view_html":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO","download_json":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO.json","view_paper":"https://pith.science/paper/MZ4HSCHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0562&json=true","fetch_graph":"https://pith.science/api/pith-number/MZ4HSCHSA6F7YE2OBFDFWSQKKO/graph.json","fetch_events":"https://pith.science/api/pith-number/MZ4HSCHSA6F7YE2OBFDFWSQKKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO/action/storage_attestation","attest_author":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO/action/author_attestation","sign_citation":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO/action/citation_signature","submit_replication":"https://pith.science/pith/MZ4HSCHSA6F7YE2OBFDFWSQKKO/action/replication_record"}},"created_at":"2026-05-18T02:09:20.765627+00:00","updated_at":"2026-05-18T02:09:20.765627+00:00"}