{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2S6MYX7WP4HICHYYWONB6IE3UP","short_pith_number":"pith:2S6MYX7W","canonical_record":{"source":{"id":"1811.05438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-11-13T18:04:53Z","cross_cats_sorted":["cs.CC","cs.MA"],"title_canon_sha256":"cb157e44c755315cb328609144a018fb2077421b05c29f90745d8fb5b6c6ed71","abstract_canon_sha256":"06fe04e0fe9425c075941c156d70c5bbbc6426c092686684e3e052bd963ca52a"},"schema_version":"1.0"},"canonical_sha256":"d4bccc5ff67f0e811f18b39a1f209ba3e7a78f03e08f5b2bfc8117476b676d5a","source":{"kind":"arxiv","id":"1811.05438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05438","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05438v1","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05438","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"2S6MYX7WP4HI","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2S6MYX7WP4HICHYY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2S6MYX7W","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2S6MYX7WP4HICHYYWONB6IE3UP","target":"record","payload":{"canonical_record":{"source":{"id":"1811.05438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-11-13T18:04:53Z","cross_cats_sorted":["cs.CC","cs.MA"],"title_canon_sha256":"cb157e44c755315cb328609144a018fb2077421b05c29f90745d8fb5b6c6ed71","abstract_canon_sha256":"06fe04e0fe9425c075941c156d70c5bbbc6426c092686684e3e052bd963ca52a"},"schema_version":"1.0"},"canonical_sha256":"d4bccc5ff67f0e811f18b39a1f209ba3e7a78f03e08f5b2bfc8117476b676d5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.153925Z","signature_b64":"8KCKgwKQF48v0976uE1SqTgXcgS+xsjlP1YPOBhLYDIhMWKcGu21EauRg3ERhgVQJFXj6I995p+Xa2HU2rFZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4bccc5ff67f0e811f18b39a1f209ba3e7a78f03e08f5b2bfc8117476b676d5a","last_reissued_at":"2026-05-18T00:00:46.153539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.153539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.05438","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":"2026-05-18T00:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JLAHDj0AO+3GXZ5zUmPxcZ3sHHPvQX13XkP3crG9/mDNOC1f2iIfkwdLvWjvr+1ZlP+rzHYfKNqFjPATf7duDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:57:58.464597Z"},"content_sha256":"379b834b9b2e4830e559eb0da5fe6137bdb71c3017d9b568ad57d55ad3cb3e67","schema_version":"1.0","event_id":"sha256:379b834b9b2e4830e559eb0da5fe6137bdb71c3017d9b568ad57d55ad3cb3e67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2S6MYX7WP4HICHYYWONB6IE3UP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Very Hard Electoral Control Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.MA"],"primary_cat":"cs.GT","authors_text":"Alexander Hoover, David E. Narv\\'aez, Edith Hemaspaandra, Zack Fitzsimmons","submitted_at":"2018-11-13T18:04:53Z","abstract_excerpt":"It is important to understand how the outcome of an election can be modified by an agent with control over the structure of the election. Electoral control has been studied for many election systems, but for all studied systems the winner problem is in P, and so control is in NP. There are election systems, such as Kemeny, that have many desirable properties, but whose winner problems are not in NP. Thus for such systems control is not in NP, and in fact we show that it is typically complete for $\\Sigma_2^p$ (i.e., ${\\rm NP}^{\\rm NP}$, the second level of the polynomial hierarchy). This is a v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05438","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":"2026-05-18T00:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wu6+1nnR1u8+p1lKIsv7TE6bI4KJdBUdb+9W3BJRhVpCUnInPegLHXdgyJO1lO6uP0eXyviUG/03SzpEcmV6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:57:58.465307Z"},"content_sha256":"098a64080d67c1d65f26686a708dec68b9c54c636f00ca3d22ded6e477c67321","schema_version":"1.0","event_id":"sha256:098a64080d67c1d65f26686a708dec68b9c54c636f00ca3d22ded6e477c67321"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2S6MYX7WP4HICHYYWONB6IE3UP/bundle.json","state_url":"https://pith.science/pith/2S6MYX7WP4HICHYYWONB6IE3UP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2S6MYX7WP4HICHYYWONB6IE3UP/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":"2026-05-27T14:57:58Z","links":{"resolver":"https://pith.science/pith/2S6MYX7WP4HICHYYWONB6IE3UP","bundle":"https://pith.science/pith/2S6MYX7WP4HICHYYWONB6IE3UP/bundle.json","state":"https://pith.science/pith/2S6MYX7WP4HICHYYWONB6IE3UP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2S6MYX7WP4HICHYYWONB6IE3UP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2S6MYX7WP4HICHYYWONB6IE3UP","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":"06fe04e0fe9425c075941c156d70c5bbbc6426c092686684e3e052bd963ca52a","cross_cats_sorted":["cs.CC","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-11-13T18:04:53Z","title_canon_sha256":"cb157e44c755315cb328609144a018fb2077421b05c29f90745d8fb5b6c6ed71"},"schema_version":"1.0","source":{"id":"1811.05438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05438","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05438v1","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05438","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"2S6MYX7WP4HI","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2S6MYX7WP4HICHYY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2S6MYX7W","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:098a64080d67c1d65f26686a708dec68b9c54c636f00ca3d22ded6e477c67321","target":"graph","created_at":"2026-05-18T00:00:46Z","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":"It is important to understand how the outcome of an election can be modified by an agent with control over the structure of the election. Electoral control has been studied for many election systems, but for all studied systems the winner problem is in P, and so control is in NP. There are election systems, such as Kemeny, that have many desirable properties, but whose winner problems are not in NP. Thus for such systems control is not in NP, and in fact we show that it is typically complete for $\\Sigma_2^p$ (i.e., ${\\rm NP}^{\\rm NP}$, the second level of the polynomial hierarchy). This is a v","authors_text":"Alexander Hoover, David E. Narv\\'aez, Edith Hemaspaandra, Zack Fitzsimmons","cross_cats":["cs.CC","cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-11-13T18:04:53Z","title":"Very Hard Electoral Control Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05438","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":"sha256:379b834b9b2e4830e559eb0da5fe6137bdb71c3017d9b568ad57d55ad3cb3e67","target":"record","created_at":"2026-05-18T00:00:46Z","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":"06fe04e0fe9425c075941c156d70c5bbbc6426c092686684e3e052bd963ca52a","cross_cats_sorted":["cs.CC","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-11-13T18:04:53Z","title_canon_sha256":"cb157e44c755315cb328609144a018fb2077421b05c29f90745d8fb5b6c6ed71"},"schema_version":"1.0","source":{"id":"1811.05438","kind":"arxiv","version":1}},"canonical_sha256":"d4bccc5ff67f0e811f18b39a1f209ba3e7a78f03e08f5b2bfc8117476b676d5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4bccc5ff67f0e811f18b39a1f209ba3e7a78f03e08f5b2bfc8117476b676d5a","first_computed_at":"2026-05-18T00:00:46.153539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:46.153539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8KCKgwKQF48v0976uE1SqTgXcgS+xsjlP1YPOBhLYDIhMWKcGu21EauRg3ERhgVQJFXj6I995p+Xa2HU2rFZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:46.153925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:379b834b9b2e4830e559eb0da5fe6137bdb71c3017d9b568ad57d55ad3cb3e67","sha256:098a64080d67c1d65f26686a708dec68b9c54c636f00ca3d22ded6e477c67321"],"state_sha256":"a0b0f87c11c278c4c279c4b01de9d3be5e11507b70b126227b21fe822f9712c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FKNVl9DZVOoiPwaHGkSk6XqKi//Mat+xEjxGncDu566SwI1ENCTGI/y0hQhmXRx8Kc0vxNgMa6IJPYX92gq1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:57:58.469474Z","bundle_sha256":"1000d386daf01a776931f52bbfd72639c5c32a391d238792b2d117c75eebf007"}}