{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FZDYEQOCS7CFJBV6UWJZQTYMLZ","short_pith_number":"pith:FZDYEQOC","canonical_record":{"source":{"id":"1307.1252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","cross_cats_sorted":["cs.MA"],"title_canon_sha256":"543145c8139ae59ba0b8054bb00b669f9af48b7a02303c1fd0cec833d9ceb2f7","abstract_canon_sha256":"1eab8d42cf3fec01f1875d4d7748c0a22729055fe54a66f907ff1cf3b3be0360"},"schema_version":"1.0"},"canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","source":{"kind":"arxiv","id":"1307.1252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1252","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1252v1","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1252","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"FZDYEQOCS7CF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZDYEQOCS7CFJBV6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZDYEQOC","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FZDYEQOCS7CFJBV6UWJZQTYMLZ","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","cross_cats_sorted":["cs.MA"],"title_canon_sha256":"543145c8139ae59ba0b8054bb00b669f9af48b7a02303c1fd0cec833d9ceb2f7","abstract_canon_sha256":"1eab8d42cf3fec01f1875d4d7748c0a22729055fe54a66f907ff1cf3b3be0360"},"schema_version":"1.0"},"canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:14.284897Z","signature_b64":"rriYdNVVTCP7xRAakf7AQLpdqEDWeasnnHd2LBuxl3lTvgD2aJwb3OTDa7GiK8nE1zbWIqGsPA+96aqrbHmxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","last_reissued_at":"2026-05-18T03:19:14.284087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:14.284087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1252","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":"2026-05-18T03:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGZW/w4zoEH1rslZoqmxFC1WNKiv0zVw4pGPQ2tU0Vi2sj3Tc4GSW+QLk/kZd3VRf0UvJpVercWPho0x0QF+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:12.589702Z"},"content_sha256":"62a8adf2d264bf8f405adb18949a30eb3adb0b053d949c497303d50acf0b4275","schema_version":"1.0","event_id":"sha256:62a8adf2d264bf8f405adb18949a30eb3adb0b053d949c497303d50acf0b4275"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FZDYEQOCS7CFJBV6UWJZQTYMLZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complexity of Fully Proportional Representation for Single-Crossing Electorates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"cs.GT","authors_text":"Edith Elkind, Lan Yu, Piotr Faliszewski, Piotr Skowron","submitted_at":"2013-07-04T09:33:24Z","abstract_excerpt":"We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1252","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":"2026-05-18T03:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hrRYTgueBLGhkxShyyGAnEkQNvJ924YYuL9z09euIdhf6svt8JH95/1T6SXD416FF/hN7vGCOmrv7HYL95RZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:12.590049Z"},"content_sha256":"938345054861a214f2c095bf8f12075567ba3fd337d24c78fedad0fb4370fb81","schema_version":"1.0","event_id":"sha256:938345054861a214f2c095bf8f12075567ba3fd337d24c78fedad0fb4370fb81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/bundle.json","state_url":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/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":"2026-06-02T04:15:12Z","links":{"resolver":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ","bundle":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/bundle.json","state":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FZDYEQOCS7CFJBV6UWJZQTYMLZ","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":"1eab8d42cf3fec01f1875d4d7748c0a22729055fe54a66f907ff1cf3b3be0360","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","title_canon_sha256":"543145c8139ae59ba0b8054bb00b669f9af48b7a02303c1fd0cec833d9ceb2f7"},"schema_version":"1.0","source":{"id":"1307.1252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1252","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1252v1","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1252","created_at":"2026-05-18T03:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"FZDYEQOCS7CF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZDYEQOCS7CFJBV6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZDYEQOC","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:938345054861a214f2c095bf8f12075567ba3fd337d24c78fedad0fb4370fb81","target":"graph","created_at":"2026-05-18T03:19:14Z","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 study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe","authors_text":"Edith Elkind, Lan Yu, Piotr Faliszewski, Piotr Skowron","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","title":"The Complexity of Fully Proportional Representation for Single-Crossing Electorates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1252","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":"sha256:62a8adf2d264bf8f405adb18949a30eb3adb0b053d949c497303d50acf0b4275","target":"record","created_at":"2026-05-18T03:19:14Z","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":"1eab8d42cf3fec01f1875d4d7748c0a22729055fe54a66f907ff1cf3b3be0360","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","title_canon_sha256":"543145c8139ae59ba0b8054bb00b669f9af48b7a02303c1fd0cec833d9ceb2f7"},"schema_version":"1.0","source":{"id":"1307.1252","kind":"arxiv","version":1}},"canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","first_computed_at":"2026-05-18T03:19:14.284087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:14.284087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rriYdNVVTCP7xRAakf7AQLpdqEDWeasnnHd2LBuxl3lTvgD2aJwb3OTDa7GiK8nE1zbWIqGsPA+96aqrbHmxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:14.284897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62a8adf2d264bf8f405adb18949a30eb3adb0b053d949c497303d50acf0b4275","sha256:938345054861a214f2c095bf8f12075567ba3fd337d24c78fedad0fb4370fb81"],"state_sha256":"969b917860d8ca6b5b57bfb0b3290dfcf8fae7bc29134d0e1fd2681c70ddcaa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ulrD4oKd293Bw19HIMEirrD0jUuEz23+se8jPcIGnKcho8z4SlEio4XzRzUDDODjcZvzMyU2RUtj/V54cp6oAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:15:12.591978Z","bundle_sha256":"9c0a51951774fcfa5214791726d72beefd1cfa026199a1128f8b8411fe936ec0"}}