{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MPN2Y4YEXZGO2CAVNYXZOA7SIX","short_pith_number":"pith:MPN2Y4YE","canonical_record":{"source":{"id":"1205.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-10T03:34:21Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"aec8b33cf887ceff8a2398024a1fb3fb667bc1f6717749006c7a1cd521ea8d8a","abstract_canon_sha256":"0e1e9481b0897f06eb7bead7089f7b6e097afb1e2899d027f901602287f5e038"},"schema_version":"1.0"},"canonical_sha256":"63dbac7304be4ced08156e2f9703f245e9bfef3c17a61be370038f62a7a59cd3","source":{"kind":"arxiv","id":"1205.2152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2152","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2152v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2152","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"MPN2Y4YEXZGO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MPN2Y4YEXZGO2CAV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MPN2Y4YE","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MPN2Y4YEXZGO2CAVNYXZOA7SIX","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-10T03:34:21Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"aec8b33cf887ceff8a2398024a1fb3fb667bc1f6717749006c7a1cd521ea8d8a","abstract_canon_sha256":"0e1e9481b0897f06eb7bead7089f7b6e097afb1e2899d027f901602287f5e038"},"schema_version":"1.0"},"canonical_sha256":"63dbac7304be4ced08156e2f9703f245e9bfef3c17a61be370038f62a7a59cd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:56.925412Z","signature_b64":"zKuxifoWsHa7AOny1rXuflucNXNSaU9w8e1bqIIYJd1ShrVkwKfQ5SlzOFR6gztW7JXz+81WpFZsIwYlfJrmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63dbac7304be4ced08156e2f9703f245e9bfef3c17a61be370038f62a7a59cd3","last_reissued_at":"2026-05-18T03:55:56.924715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:56.924715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2152","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JD8HE2WGuKH/JwBG4iHHYBe/8/IKRSrOHwg6dv6H3WEvKKw9CO75dfs78jEINgpBj2Uee2ptzzHawA/coYqvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:32:03.747017Z"},"content_sha256":"328d0971ad21b8fb5523032dda1c21e0541a07b37cd12d8b26a1bc39234fc140","schema_version":"1.0","event_id":"sha256:328d0971ad21b8fb5523032dda1c21e0541a07b37cd12d8b26a1bc39234fc140"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MPN2Y4YEXZGO2CAVNYXZOA7SIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Roughly Weighted Hierarchical Simple Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"math.CO","authors_text":"Ali Hameed, Arkadii Slinko","submitted_at":"2012-05-10T03:34:21Z","abstract_excerpt":"Hierarchical simple games - both disjunctive and conjunctive - are natural generalizations of simple majority games. They take their origin in the theory of secret sharing. Another important generalization of simple majority games with origin in economics and politics are weighted and roughly weighted majority games. In this paper we characterize roughly weighted hierarchical games identifying where the two approaches coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2152","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxPlRcT5pCYfIPv9SM/S+pepMq9IFclYIghiDsq0u8WDlruXnLdTPYB/KC+plJXTvekbw1I/1LdkYrwKUJOhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:32:03.747635Z"},"content_sha256":"6609542e081cab4809caa146996f08ecaae3a7b393dab8184d0f0e6176090fba","schema_version":"1.0","event_id":"sha256:6609542e081cab4809caa146996f08ecaae3a7b393dab8184d0f0e6176090fba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/bundle.json","state_url":"https://pith.science/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T23:32:03Z","links":{"resolver":"https://pith.science/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX","bundle":"https://pith.science/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/bundle.json","state":"https://pith.science/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPN2Y4YEXZGO2CAVNYXZOA7SIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MPN2Y4YEXZGO2CAVNYXZOA7SIX","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":"0e1e9481b0897f06eb7bead7089f7b6e097afb1e2899d027f901602287f5e038","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-10T03:34:21Z","title_canon_sha256":"aec8b33cf887ceff8a2398024a1fb3fb667bc1f6717749006c7a1cd521ea8d8a"},"schema_version":"1.0","source":{"id":"1205.2152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2152","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2152v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2152","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"MPN2Y4YEXZGO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MPN2Y4YEXZGO2CAV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MPN2Y4YE","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:6609542e081cab4809caa146996f08ecaae3a7b393dab8184d0f0e6176090fba","target":"graph","created_at":"2026-05-18T03:55:56Z","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":"Hierarchical simple games - both disjunctive and conjunctive - are natural generalizations of simple majority games. They take their origin in the theory of secret sharing. Another important generalization of simple majority games with origin in economics and politics are weighted and roughly weighted majority games. In this paper we characterize roughly weighted hierarchical games identifying where the two approaches coincide.","authors_text":"Ali Hameed, Arkadii Slinko","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-10T03:34:21Z","title":"Roughly Weighted Hierarchical Simple Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2152","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":"sha256:328d0971ad21b8fb5523032dda1c21e0541a07b37cd12d8b26a1bc39234fc140","target":"record","created_at":"2026-05-18T03:55:56Z","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":"0e1e9481b0897f06eb7bead7089f7b6e097afb1e2899d027f901602287f5e038","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-10T03:34:21Z","title_canon_sha256":"aec8b33cf887ceff8a2398024a1fb3fb667bc1f6717749006c7a1cd521ea8d8a"},"schema_version":"1.0","source":{"id":"1205.2152","kind":"arxiv","version":1}},"canonical_sha256":"63dbac7304be4ced08156e2f9703f245e9bfef3c17a61be370038f62a7a59cd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63dbac7304be4ced08156e2f9703f245e9bfef3c17a61be370038f62a7a59cd3","first_computed_at":"2026-05-18T03:55:56.924715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:56.924715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zKuxifoWsHa7AOny1rXuflucNXNSaU9w8e1bqIIYJd1ShrVkwKfQ5SlzOFR6gztW7JXz+81WpFZsIwYlfJrmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:56.925412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:328d0971ad21b8fb5523032dda1c21e0541a07b37cd12d8b26a1bc39234fc140","sha256:6609542e081cab4809caa146996f08ecaae3a7b393dab8184d0f0e6176090fba"],"state_sha256":"08e7039b764ee55390773a2b850e31ae94200a2cfaec9f137815cbe29525291e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LJtDwqyOFcEQXEV3KKu5UMivWiYzxsIA3pxuZFaiOdHV0ycdoGTGtbNfb1L7yjPwu0rtYTdHum8fiQ0aw9BAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:32:03.751162Z","bundle_sha256":"096d035e36d56fc0fa4caf3ff206505550a3fe7e2df2293e743b6c8046a55b35"}}