{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AHCGSRQTZ25EQKP2OUIHMBSLIX","short_pith_number":"pith:AHCGSRQT","schema_version":"1.0","canonical_sha256":"01c4694613ceba4829fa751076064b45e3c8131421a5f16e5dc85e02414400e9","source":{"kind":"arxiv","id":"1805.02192","version":1},"attestation_state":"computed","paper":{"title":"Simple Games versus Weighted Voting Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Dani\\\"el Paulusma, Frits Hof, Sascha Kurz, Walter Kern","submitted_at":"2018-05-06T11:46:44Z","abstract_excerpt":"A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $\\alpha= \\min_{p\\geq 0}\\max_{W\\in {\\cal W},L\\in {\\cal L}} \\frac{p(L)}{p(W)}<1$ are known as weighted voting games. Freixas and Kurz (IJGT, 2014) conjectured that $\\alpha\\leq \\frac{1}{4}n$ for every simple game $(N,v)$. We confirm this conjecture for two complementary cases, namely when all minimal winning coalitions have size"},"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":"1805.02192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-05-06T11:46:44Z","cross_cats_sorted":[],"title_canon_sha256":"d3082b7e63925ed80f640c51bc76537bdb7661be0c45056619786ac8c1419e46","abstract_canon_sha256":"fe1c03fc2338def7a1e1fea67768087a4ad5042a22adf573650d914ef149fd78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:56.019332Z","signature_b64":"X+oAt8e/u9iNgwJp31jLHAoaHd/VD7cMn29655pnqplYbSoEVPiY7EBZcbrAURAr23S2PA5VslVBFKNK7kpvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01c4694613ceba4829fa751076064b45e3c8131421a5f16e5dc85e02414400e9","last_reissued_at":"2026-05-18T00:06:56.018721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:56.018721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple Games versus Weighted Voting Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Dani\\\"el Paulusma, Frits Hof, Sascha Kurz, Walter Kern","submitted_at":"2018-05-06T11:46:44Z","abstract_excerpt":"A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $\\alpha= \\min_{p\\geq 0}\\max_{W\\in {\\cal W},L\\in {\\cal L}} \\frac{p(L)}{p(W)}<1$ are known as weighted voting games. Freixas and Kurz (IJGT, 2014) conjectured that $\\alpha\\leq \\frac{1}{4}n$ for every simple game $(N,v)$. We confirm this conjecture for two complementary cases, namely when all minimal winning coalitions have size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02192","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":"1805.02192","created_at":"2026-05-18T00:06:56.018816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02192v1","created_at":"2026-05-18T00:06:56.018816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02192","created_at":"2026-05-18T00:06:56.018816+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHCGSRQTZ25E","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHCGSRQTZ25EQKP2","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHCGSRQT","created_at":"2026-05-18T12:32:13.499390+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/AHCGSRQTZ25EQKP2OUIHMBSLIX","json":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX.json","graph_json":"https://pith.science/api/pith-number/AHCGSRQTZ25EQKP2OUIHMBSLIX/graph.json","events_json":"https://pith.science/api/pith-number/AHCGSRQTZ25EQKP2OUIHMBSLIX/events.json","paper":"https://pith.science/paper/AHCGSRQT"},"agent_actions":{"view_html":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX","download_json":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX.json","view_paper":"https://pith.science/paper/AHCGSRQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02192&json=true","fetch_graph":"https://pith.science/api/pith-number/AHCGSRQTZ25EQKP2OUIHMBSLIX/graph.json","fetch_events":"https://pith.science/api/pith-number/AHCGSRQTZ25EQKP2OUIHMBSLIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX/action/storage_attestation","attest_author":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX/action/author_attestation","sign_citation":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX/action/citation_signature","submit_replication":"https://pith.science/pith/AHCGSRQTZ25EQKP2OUIHMBSLIX/action/replication_record"}},"created_at":"2026-05-18T00:06:56.018816+00:00","updated_at":"2026-05-18T00:06:56.018816+00:00"}