{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QBAKEPHLNP5JX5WDDW3WM7JTFR","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":"3a85b0178b8e0ab68b7e4781f69d7a9d74d832c6b8741afabecbbf0ff0c60f50","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2024-01-23T08:09:07Z","title_canon_sha256":"9e209e574e501ee34ba27f0cce59fffbd21cb3e1c48a6cba16e36e8429938023"},"schema_version":"1.0","source":{"id":"2401.12547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12547","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12547v1","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12547","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"QBAKEPHLNP5J","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_16","alias_value":"QBAKEPHLNP5JX5WD","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_8","alias_value":"QBAKEPHL","created_at":"2026-07-05T07:36:32Z"}],"graph_snapshots":[{"event_id":"sha256:c6cca14f391b657f0016cefd9201b00311eec415159b3e2f667e35761d598219","target":"graph","created_at":"2026-07-05T07:36:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.12547/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we extend the study of Arrow's generalisation of Black's single-peaked domain and connect this to domains where voting rules satisfy different versions of independence of irrelevant alternatives.\n  First we report on a computational generation of all non-isomorphic Arrow's single-peaked domains on $n\\leq 9$ alternatives. Next, we introduce a quantitative measure of richness for domains, as the largest number $r$ such that every alternative is given every rank between 1 and $r$ by the orders in the domain. We investigate the richness of Arrow's single-peaked domains and prove that","authors_text":"Bei Zhou, Klas Markstr\\\"om, S{\\o}ren Riis","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2024-01-23T08:09:07Z","title":"Arrow's single peaked domains, richness, and domains for plurality and the Borda count"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12547","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:d41278cc5c7cda4e04b8d47c3b88208900888f730a83eb9ede1dadd6a6b06cff","target":"record","created_at":"2026-07-05T07:36:32Z","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":"3a85b0178b8e0ab68b7e4781f69d7a9d74d832c6b8741afabecbbf0ff0c60f50","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2024-01-23T08:09:07Z","title_canon_sha256":"9e209e574e501ee34ba27f0cce59fffbd21cb3e1c48a6cba16e36e8429938023"},"schema_version":"1.0","source":{"id":"2401.12547","kind":"arxiv","version":1}},"canonical_sha256":"8040a23ceb6bfa9bf6c31db7667d332c572d16946041cd03c922d6bef0572f91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8040a23ceb6bfa9bf6c31db7667d332c572d16946041cd03c922d6bef0572f91","first_computed_at":"2026-07-05T07:36:32.324068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:36:32.324068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnIUlj0tZicI+0ITZNJf/BXes/0F4x8/U9G4YLABcTQ/73ePyKjZ/pYRZBq5LF2VTv5o9UJFne8T9SKYufHLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:36:32.324502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.12547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d41278cc5c7cda4e04b8d47c3b88208900888f730a83eb9ede1dadd6a6b06cff","sha256:c6cca14f391b657f0016cefd9201b00311eec415159b3e2f667e35761d598219"],"state_sha256":"6cdd6f5190f07b89fd1d318e6d6b12c894c5be51b83291f44e4ef88a97f43a70"}