{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:IZTUFDS72XD7OCPQCNFECCWLTW","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":"1160089ae9480af098ef6009d3df8b093319d9232b35f6bc0bca841119e7945b","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-12-01T06:58:09Z","title_canon_sha256":"18e13d0c3499a547099f423d4337debb3031d0941031116b03ec8beb7e06049e"},"schema_version":"1.0","source":{"id":"2112.00307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.00307","created_at":"2026-07-05T03:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2112.00307v1","created_at":"2026-07-05T03:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.00307","created_at":"2026-07-05T03:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"IZTUFDS72XD7","created_at":"2026-07-05T03:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"IZTUFDS72XD7OCPQ","created_at":"2026-07-05T03:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"IZTUFDS7","created_at":"2026-07-05T03:36:44Z"}],"graph_snapshots":[{"event_id":"sha256:f55c7fe5b185f84c0c10dfbf8ac1de6d17ae42266cd0ab7d70942f38501b7278","target":"graph","created_at":"2026-07-05T03:36:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.00307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a {\\lq\\lq}House{\\rq\\rq} and a {\\lq\\lq}Senat{\\rq\\rq} is of that type. Here we present structural characterizations and explicit enumeration formulas for these so-called bipartite simple games.","authors_text":"Dani Samaniego, Sascha Kurz","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-12-01T06:58:09Z","title":"A note on simple games with two equivalence classes of players"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.00307","kind":"arxiv","version":1},"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:a5eb42748d12c363e0ef8681ff424bfbf19ae34275118624cddd1e7f731e036e","target":"record","created_at":"2026-07-05T03:36:44Z","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":"1160089ae9480af098ef6009d3df8b093319d9232b35f6bc0bca841119e7945b","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-12-01T06:58:09Z","title_canon_sha256":"18e13d0c3499a547099f423d4337debb3031d0941031116b03ec8beb7e06049e"},"schema_version":"1.0","source":{"id":"2112.00307","kind":"arxiv","version":1}},"canonical_sha256":"4667428e5fd5c7f709f0134a410acb9db83ee01a83a3e11c46fc1c5dbcdc1598","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4667428e5fd5c7f709f0134a410acb9db83ee01a83a3e11c46fc1c5dbcdc1598","first_computed_at":"2026-07-05T03:36:44.979953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:36:44.979953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Irt1Q0BaLwj2y5R0fLjL/txdTJumuo9CUyZXKQulobEjjc+dJEynDOxBl0k7nzTBzRYdEYILvB88i7fHCcTVAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:36:44.980408Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.00307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5eb42748d12c363e0ef8681ff424bfbf19ae34275118624cddd1e7f731e036e","sha256:f55c7fe5b185f84c0c10dfbf8ac1de6d17ae42266cd0ab7d70942f38501b7278"],"state_sha256":"c8cd2e976c8dd8f0984df22c4fc087f9fff9e38f6656b51685ade4d03c3f44f1"}