{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FFDXTHX4S4KREOPIVO4ZHKUDFW","short_pith_number":"pith:FFDXTHX4","canonical_record":{"source":{"id":"1304.4471","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-04-16T14:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"e9207a8bef88211c38a187894cc4a5edd876c61748b46095cd0e77ef88c3365e","abstract_canon_sha256":"97813e8cd9de5854351cacf35b2095b48d615e95100a61b6dca349d279b67931"},"schema_version":"1.0"},"canonical_sha256":"2947799efc97151239e8abb993aa832da0a0c823bf6aa3899156ffc4b59571cb","source":{"kind":"arxiv","id":"1304.4471","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4471","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4471v4","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4471","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"FFDXTHX4S4KR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FFDXTHX4S4KREOPI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FFDXTHX4","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FFDXTHX4S4KREOPIVO4ZHKUDFW","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4471","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-04-16T14:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"e9207a8bef88211c38a187894cc4a5edd876c61748b46095cd0e77ef88c3365e","abstract_canon_sha256":"97813e8cd9de5854351cacf35b2095b48d615e95100a61b6dca349d279b67931"},"schema_version":"1.0"},"canonical_sha256":"2947799efc97151239e8abb993aa832da0a0c823bf6aa3899156ffc4b59571cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.996154Z","signature_b64":"BzKZMrRzzwYreW7ZX4KgFNDEOZPAE1p3ffWbOtLwy0nEMQQ3+TXRVlXHwRXSPpFaikIkTGWRcYv5ZSuzD52gCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2947799efc97151239e8abb993aa832da0a0c823bf6aa3899156ffc4b59571cb","last_reissued_at":"2026-05-18T00:42:39.995496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.995496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4471","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ogjgd1sGl+8/GCaz+a7tOI/Ei23aV2CPJ74W+wIRCilp+pDsAkFFwyxorLFVQR2W3iobTqp4whRODmXuq8TQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:35:20.715858Z"},"content_sha256":"69af4020243cda555dc5b3ae58c5019aade1571a9ff9728ec78835695beb1d56","schema_version":"1.0","event_id":"sha256:69af4020243cda555dc5b3ae58c5019aade1571a9ff9728ec78835695beb1d56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FFDXTHX4S4KREOPIVO4ZHKUDFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Control Complexity of $r$-Approval: from the Single-Peaked Case to the General Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Jiong Guo, Yongjie Yang","submitted_at":"2013-04-16T14:41:44Z","abstract_excerpt":"We investigate the complexity of $r$-Approval control problems in $k$-peaked elections, where at most $k$ peaks are allowed in each vote with respect to an order of the candidates. We show that most NP-hardness results in general elections also hold in k-peaked elections even for $k=2,3$. On the other hand, we derive polynomial-time algorithms for some problems for $k=2$. All our NP-hardness results apply to Approval and sincere-strategy preference-based Approval as well. Our study leads to many dichotomy results for the problems considered in this paper, with respect to the values of $k$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4471","kind":"arxiv","version":4},"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":"2026-05-18T00:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3+NpbJvUlTmMpgyG0uEd+0ow2QkRpYX3yWy4BNpStZC6qHq+nhuQ6qxGSFslguFQR7pO5aFy6Gm9f4joWHpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:35:20.716610Z"},"content_sha256":"15e12688f06b6890c03dcc40af70a01c9bbfb52682cdf9ef08eab581405713a0","schema_version":"1.0","event_id":"sha256:15e12688f06b6890c03dcc40af70a01c9bbfb52682cdf9ef08eab581405713a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/bundle.json","state_url":"https://pith.science/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/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":"2026-06-06T16:35:20Z","links":{"resolver":"https://pith.science/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW","bundle":"https://pith.science/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/bundle.json","state":"https://pith.science/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFDXTHX4S4KREOPIVO4ZHKUDFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FFDXTHX4S4KREOPIVO4ZHKUDFW","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":"97813e8cd9de5854351cacf35b2095b48d615e95100a61b6dca349d279b67931","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-04-16T14:41:44Z","title_canon_sha256":"e9207a8bef88211c38a187894cc4a5edd876c61748b46095cd0e77ef88c3365e"},"schema_version":"1.0","source":{"id":"1304.4471","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4471","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4471v4","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4471","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"FFDXTHX4S4KR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FFDXTHX4S4KREOPI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FFDXTHX4","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:15e12688f06b6890c03dcc40af70a01c9bbfb52682cdf9ef08eab581405713a0","target":"graph","created_at":"2026-05-18T00:42:39Z","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":"We investigate the complexity of $r$-Approval control problems in $k$-peaked elections, where at most $k$ peaks are allowed in each vote with respect to an order of the candidates. We show that most NP-hardness results in general elections also hold in k-peaked elections even for $k=2,3$. On the other hand, we derive polynomial-time algorithms for some problems for $k=2$. All our NP-hardness results apply to Approval and sincere-strategy preference-based Approval as well. Our study leads to many dichotomy results for the problems considered in this paper, with respect to the values of $k$ and ","authors_text":"Jiong Guo, Yongjie Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-04-16T14:41:44Z","title":"The Control Complexity of $r$-Approval: from the Single-Peaked Case to the General Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4471","kind":"arxiv","version":4},"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":"sha256:69af4020243cda555dc5b3ae58c5019aade1571a9ff9728ec78835695beb1d56","target":"record","created_at":"2026-05-18T00:42:39Z","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":"97813e8cd9de5854351cacf35b2095b48d615e95100a61b6dca349d279b67931","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-04-16T14:41:44Z","title_canon_sha256":"e9207a8bef88211c38a187894cc4a5edd876c61748b46095cd0e77ef88c3365e"},"schema_version":"1.0","source":{"id":"1304.4471","kind":"arxiv","version":4}},"canonical_sha256":"2947799efc97151239e8abb993aa832da0a0c823bf6aa3899156ffc4b59571cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2947799efc97151239e8abb993aa832da0a0c823bf6aa3899156ffc4b59571cb","first_computed_at":"2026-05-18T00:42:39.995496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:39.995496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BzKZMrRzzwYreW7ZX4KgFNDEOZPAE1p3ffWbOtLwy0nEMQQ3+TXRVlXHwRXSPpFaikIkTGWRcYv5ZSuzD52gCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:39.996154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4471","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69af4020243cda555dc5b3ae58c5019aade1571a9ff9728ec78835695beb1d56","sha256:15e12688f06b6890c03dcc40af70a01c9bbfb52682cdf9ef08eab581405713a0"],"state_sha256":"3ffbf6ccc54c4de150e55cdb7ea558a193a1badd4c21841a2fbec3a05c9fd1a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJkQwycWqoFt6tiPi+I35WezFOULGbGZPb+gXLP/4if2GXAYvIfy1UHYPZFcslwg1U3SBYcXVMqemqyXhCsuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:35:20.720339Z","bundle_sha256":"4e0957ee43951cb78f114d72d8592012f622608dbeb4b4d76dc69bab97684118"}}