{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DDZCCCYSWZJ7CPK6UP7EEJOOUE","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":"7d7092341dc2ba434310335ae359f88022c997552a7e89a2559524bb54078cdb","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-03T18:32:08Z","title_canon_sha256":"7a015eb83dd207b11ec2b6e40c07ba8779da817e64106f688d1784729116813f"},"schema_version":"1.0","source":{"id":"1207.0773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0773","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0773v2","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0773","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"DDZCCCYSWZJ7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DDZCCCYSWZJ7CPK6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DDZCCCYS","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:5614949f7d592fa80c6e3d99d70888c73371e3c7b05d2372b90e5c31a2205f6e","target":"graph","created_at":"2026-05-18T03:36:15Z","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":"We analyze the general version of the classic guessing game Mastermind with $n$ positions and $k$ colors. Since the case $k \\le n^{1-\\varepsilon}$, $\\varepsilon>0$ a constant, is well understood, we concentrate on larger numbers of colors. For the most prominent case $k = n$, our results imply that Codebreaker can find the secret code with $O(n \\log \\log n)$ guesses. This bound is valid also when only black answer-pegs are used. It improves the $O(n \\log n)$ bound first proven by Chv\\'atal (Combinatorica 3 (1983), 325--329). We also show that if both black and white answer-pegs are used, then ","authors_text":"Benjamin Doerr, Carola Doerr, Henning Thomas, Reto Sp\\\"ohel","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-03T18:32:08Z","title":"Playing Mastermind with Many Colors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0773","kind":"arxiv","version":2},"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":"sha256:29e2c2348cb3ae4a93b223d7e0c41387fb215f9e9dea7f9ddf4e2150047070c9","target":"record","created_at":"2026-05-18T03:36:15Z","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":"7d7092341dc2ba434310335ae359f88022c997552a7e89a2559524bb54078cdb","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-03T18:32:08Z","title_canon_sha256":"7a015eb83dd207b11ec2b6e40c07ba8779da817e64106f688d1784729116813f"},"schema_version":"1.0","source":{"id":"1207.0773","kind":"arxiv","version":2}},"canonical_sha256":"18f2210b12b653f13d5ea3fe4225cea11811652d350cb7422cc4c28965bcc4ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18f2210b12b653f13d5ea3fe4225cea11811652d350cb7422cc4c28965bcc4ce","first_computed_at":"2026-05-18T03:36:15.965946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:15.965946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMYAT7QxmAQXGK/XX3Pn8XsnxKURtjwjaTsiam533S6z+h93YG68eOiGQzh3FNr8IdXV3i26MDMVjygQbrwKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:15.966616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29e2c2348cb3ae4a93b223d7e0c41387fb215f9e9dea7f9ddf4e2150047070c9","sha256:5614949f7d592fa80c6e3d99d70888c73371e3c7b05d2372b90e5c31a2205f6e"],"state_sha256":"e71f453768b97ebd5b232c1a1396b61d8a6c4ba707edc1d5656a6b37a1c80f95"}