{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SKMYLHGPAPKSALZ7H5LL3YUBUH","short_pith_number":"pith:SKMYLHGP","schema_version":"1.0","canonical_sha256":"9299859ccf03d5202f3f3f56bde281a1f01d4cfd2bb52bfb19d45bfcd6b344ec","source":{"kind":"arxiv","id":"1402.5913","version":1},"attestation_state":"computed","paper":{"title":"The majority game with an arbitrary majority","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2014-02-24T18:10:28Z","abstract_excerpt":"The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player selects two balls to compare, and it is revealed whether they are of the same colour; the player's aim is to determine a ball of the majority colour. It has been correctly stated by Aigner that the minimum number of comparisons necessary to guarantee success is $2(n-k) - B(n-k)$, where $B(m)$ is the weight of the binary expansion of $m$. However his proof con"},"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":"1402.5913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-24T18:10:28Z","cross_cats_sorted":[],"title_canon_sha256":"eba05d127123e4b4f26fae99b142bddb54b7b60afadbcad984f999536b996b27","abstract_canon_sha256":"f930ffd44a9ae4b2235fd78511995c34ea10e84c7155e524b7aa297313253836"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:12.872187Z","signature_b64":"XrADLcmQCzmDEA///ZTJa5QZ/kmp4rI3bOMKCw1vCw5mK+B+F4kUIBp6NcEF4DNAFPOa/fwZ6hJdHdNiYodEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9299859ccf03d5202f3f3f56bde281a1f01d4cfd2bb52bfb19d45bfcd6b344ec","last_reissued_at":"2026-05-18T02:58:12.871443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:12.871443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The majority game with an arbitrary majority","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2014-02-24T18:10:28Z","abstract_excerpt":"The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player selects two balls to compare, and it is revealed whether they are of the same colour; the player's aim is to determine a ball of the majority colour. It has been correctly stated by Aigner that the minimum number of comparisons necessary to guarantee success is $2(n-k) - B(n-k)$, where $B(m)$ is the weight of the binary expansion of $m$. However his proof con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5913","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":"1402.5913","created_at":"2026-05-18T02:58:12.871562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.5913v1","created_at":"2026-05-18T02:58:12.871562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5913","created_at":"2026-05-18T02:58:12.871562+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKMYLHGPAPKS","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKMYLHGPAPKSALZ7","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKMYLHGP","created_at":"2026-05-18T12:28:49.207871+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/SKMYLHGPAPKSALZ7H5LL3YUBUH","json":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH.json","graph_json":"https://pith.science/api/pith-number/SKMYLHGPAPKSALZ7H5LL3YUBUH/graph.json","events_json":"https://pith.science/api/pith-number/SKMYLHGPAPKSALZ7H5LL3YUBUH/events.json","paper":"https://pith.science/paper/SKMYLHGP"},"agent_actions":{"view_html":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH","download_json":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH.json","view_paper":"https://pith.science/paper/SKMYLHGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.5913&json=true","fetch_graph":"https://pith.science/api/pith-number/SKMYLHGPAPKSALZ7H5LL3YUBUH/graph.json","fetch_events":"https://pith.science/api/pith-number/SKMYLHGPAPKSALZ7H5LL3YUBUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH/action/storage_attestation","attest_author":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH/action/author_attestation","sign_citation":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH/action/citation_signature","submit_replication":"https://pith.science/pith/SKMYLHGPAPKSALZ7H5LL3YUBUH/action/replication_record"}},"created_at":"2026-05-18T02:58:12.871562+00:00","updated_at":"2026-05-18T02:58:12.871562+00:00"}