{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SSUIUNL3CQYCNHOIMPEDPE3RUH","short_pith_number":"pith:SSUIUNL3","canonical_record":{"source":{"id":"1105.5129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-25T19:51:50Z","cross_cats_sorted":["cs.AI","math.PR"],"title_canon_sha256":"990ebb07b02f9f10ece6a0a31e534548944ff438cbbc38d5d5374284b28415cc","abstract_canon_sha256":"f87750f564612c60de121bad2477dec82d69fedbc22f853965e43e732af8da22"},"schema_version":"1.0"},"canonical_sha256":"94a88a357b1430269dc863c8379371a1e1fb5ae89c93b49fb3ffad2be0ed2827","source":{"kind":"arxiv","id":"1105.5129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5129","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5129v1","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5129","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"SSUIUNL3CQYC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SSUIUNL3CQYCNHOI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SSUIUNL3","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SSUIUNL3CQYCNHOIMPEDPE3RUH","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-25T19:51:50Z","cross_cats_sorted":["cs.AI","math.PR"],"title_canon_sha256":"990ebb07b02f9f10ece6a0a31e534548944ff438cbbc38d5d5374284b28415cc","abstract_canon_sha256":"f87750f564612c60de121bad2477dec82d69fedbc22f853965e43e732af8da22"},"schema_version":"1.0"},"canonical_sha256":"94a88a357b1430269dc863c8379371a1e1fb5ae89c93b49fb3ffad2be0ed2827","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:20.791597Z","signature_b64":"CICdI69/5QN0aEru+l0LdJ36dTo2eYrQOFuQuZfHm2z0xzxYPf5NU8wADWobawftYCbmwEkuBqzLiQWaa5SHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94a88a357b1430269dc863c8379371a1e1fb5ae89c93b49fb3ffad2be0ed2827","last_reissued_at":"2026-05-18T04:21:20.791167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:20.791167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5129","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":"2026-05-18T04:21:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qZFuOI6KTUVKPGSAM8q4jXMInhQ+avY4yZDIp0Z0S3fBYcJ7Icw8uR2/H/9T7ZoYIRanWQQRsBDnAmLdA0UNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:07.697895Z"},"content_sha256":"eacd77b19039507d675a72af7d98bb05f6230cf943fa524890fb78eb1ef34545","schema_version":"1.0","event_id":"sha256:eacd77b19039507d675a72af7d98bb05f6230cf943fa524890fb78eb1ef34545"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SSUIUNL3CQYCNHOIMPEDPE3RUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.PR"],"primary_cat":"math.CO","authors_text":"Ehud Friedgut, Gil Kalai, Nathan Keller, Noam Nisan","submitted_at":"2011-05-25T19:51:50Z","abstract_excerpt":"The Gibbard-Satterthwaite theorem states that every non-dictatorial election rule among at least three alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with a non-negligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5129","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":"2026-05-18T04:21:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXqjADXtGkMF1KMyacr2WyI6BfdozfManW3aDfIhHsKgDDeqfUKHbCge7n3MB/Ku2eO+AYAg7rdC8FDcbNPGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:07.698677Z"},"content_sha256":"e4ad558c2119e84f142bc730806e2366e9427346bc8c6fd8a094279fb638d271","schema_version":"1.0","event_id":"sha256:e4ad558c2119e84f142bc730806e2366e9427346bc8c6fd8a094279fb638d271"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/bundle.json","state_url":"https://pith.science/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/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":"2026-06-09T17:09:07Z","links":{"resolver":"https://pith.science/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH","bundle":"https://pith.science/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/bundle.json","state":"https://pith.science/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSUIUNL3CQYCNHOIMPEDPE3RUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SSUIUNL3CQYCNHOIMPEDPE3RUH","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":"f87750f564612c60de121bad2477dec82d69fedbc22f853965e43e732af8da22","cross_cats_sorted":["cs.AI","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-25T19:51:50Z","title_canon_sha256":"990ebb07b02f9f10ece6a0a31e534548944ff438cbbc38d5d5374284b28415cc"},"schema_version":"1.0","source":{"id":"1105.5129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5129","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5129v1","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5129","created_at":"2026-05-18T04:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"SSUIUNL3CQYC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SSUIUNL3CQYCNHOI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SSUIUNL3","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:e4ad558c2119e84f142bc730806e2366e9427346bc8c6fd8a094279fb638d271","target":"graph","created_at":"2026-05-18T04:21:20Z","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":"The Gibbard-Satterthwaite theorem states that every non-dictatorial election rule among at least three alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with a non-negligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range.","authors_text":"Ehud Friedgut, Gil Kalai, Nathan Keller, Noam Nisan","cross_cats":["cs.AI","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-25T19:51:50Z","title":"A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5129","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:eacd77b19039507d675a72af7d98bb05f6230cf943fa524890fb78eb1ef34545","target":"record","created_at":"2026-05-18T04:21:20Z","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":"f87750f564612c60de121bad2477dec82d69fedbc22f853965e43e732af8da22","cross_cats_sorted":["cs.AI","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-25T19:51:50Z","title_canon_sha256":"990ebb07b02f9f10ece6a0a31e534548944ff438cbbc38d5d5374284b28415cc"},"schema_version":"1.0","source":{"id":"1105.5129","kind":"arxiv","version":1}},"canonical_sha256":"94a88a357b1430269dc863c8379371a1e1fb5ae89c93b49fb3ffad2be0ed2827","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a88a357b1430269dc863c8379371a1e1fb5ae89c93b49fb3ffad2be0ed2827","first_computed_at":"2026-05-18T04:21:20.791167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:20.791167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CICdI69/5QN0aEru+l0LdJ36dTo2eYrQOFuQuZfHm2z0xzxYPf5NU8wADWobawftYCbmwEkuBqzLiQWaa5SHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:20.791597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eacd77b19039507d675a72af7d98bb05f6230cf943fa524890fb78eb1ef34545","sha256:e4ad558c2119e84f142bc730806e2366e9427346bc8c6fd8a094279fb638d271"],"state_sha256":"50bf54652765b493a32d973520d17eb5275306f664ecacf6ae819d7baae59ba1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5+pSVaceWqW2zK5jRA0/1Hgi3UUgl1urtd9JRYMaMcHAYceTRR5oYrwa3j7HhVQosUFO6AlvZOa7b+CvB7KDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:09:07.702552Z","bundle_sha256":"51cb933481cebb6ba7b4fdd9839d52d69a2f002ebc582bd546028e5065bc3a18"}}