{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LC3ELDPN6WRDFCV55IRQUG6DNE","short_pith_number":"pith:LC3ELDPN","canonical_record":{"source":{"id":"0910.2465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-13T20:01:35Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"5dbfcaaa9ab6fe5f3b433370dccf424c0b2efed52d160a03fc57653cb2b4c7c6","abstract_canon_sha256":"316bfd89ac4ef7abf14fa231a851715d993a1608615c97f8664f20d8013100bc"},"schema_version":"1.0"},"canonical_sha256":"58b6458dedf5a2328abdea230a1bc3692fa7db039a39535c2491f1648c7ef726","source":{"kind":"arxiv","id":"0910.2465","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2465","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2465v2","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2465","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"LC3ELDPN6WRD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LC3ELDPN6WRDFCV5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LC3ELDPN","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LC3ELDPN6WRDFCV55IRQUG6DNE","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-13T20:01:35Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"5dbfcaaa9ab6fe5f3b433370dccf424c0b2efed52d160a03fc57653cb2b4c7c6","abstract_canon_sha256":"316bfd89ac4ef7abf14fa231a851715d993a1608615c97f8664f20d8013100bc"},"schema_version":"1.0"},"canonical_sha256":"58b6458dedf5a2328abdea230a1bc3692fa7db039a39535c2491f1648c7ef726","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:48.290844Z","signature_b64":"+9OclOIn6cFDDVdq8BpLMmAlrcvJ+ZoP/7/fTngfzbj8WKwz4iYgU4g0QrvAHisTthZUbij2uNvVOk7MQ4bmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58b6458dedf5a2328abdea230a1bc3692fa7db039a39535c2491f1648c7ef726","last_reissued_at":"2026-05-18T00:09:48.290037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:48.290037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2465","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hY/C8e9772sebE6rHF8ONmU3ZChJk6XAaY2D22kzHHykSkNiZKruw75xDuIFUGMZV8OHn6NA1wOPuD/J945Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:08:43.114123Z"},"content_sha256":"3eb2c7f92cbbc795ff9a23be2f77bab978d26febd66f8d13943884ca192438f2","schema_version":"1.0","event_id":"sha256:3eb2c7f92cbbc795ff9a23be2f77bab978d26febd66f8d13943884ca192438f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LC3ELDPN6WRDFCV55IRQUG6DNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH"],"primary_cat":"math.CO","authors_text":"Elchanan Mossel, Omer Tamuz","submitted_at":"2009-10-13T20:01:35Z","abstract_excerpt":"Arrow's theorem implies that a social choice function satisfying Transitivity, the Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are allowed, a dictatorial social choice function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2465","kind":"arxiv","version":2},"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":"2026-05-18T00:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vb4sbkjwARgvhYvnbqrI5wtraLNx0m4y6QMAqxUMPCK/8w7l7BYAwL1KHES75wnaAWOkiyXguFkGoN4MeIZ9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:08:43.114506Z"},"content_sha256":"fd1e575b625aba0ed16fd4380a0abca660604187505034ee5bbc9c2ee6a2b3ac","schema_version":"1.0","event_id":"sha256:fd1e575b625aba0ed16fd4380a0abca660604187505034ee5bbc9c2ee6a2b3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/bundle.json","state_url":"https://pith.science/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/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":"2026-05-30T19:08:43Z","links":{"resolver":"https://pith.science/pith/LC3ELDPN6WRDFCV55IRQUG6DNE","bundle":"https://pith.science/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/bundle.json","state":"https://pith.science/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LC3ELDPN6WRDFCV55IRQUG6DNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LC3ELDPN6WRDFCV55IRQUG6DNE","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":"316bfd89ac4ef7abf14fa231a851715d993a1608615c97f8664f20d8013100bc","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-13T20:01:35Z","title_canon_sha256":"5dbfcaaa9ab6fe5f3b433370dccf424c0b2efed52d160a03fc57653cb2b4c7c6"},"schema_version":"1.0","source":{"id":"0910.2465","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2465","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2465v2","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2465","created_at":"2026-05-18T00:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"LC3ELDPN6WRD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LC3ELDPN6WRDFCV5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LC3ELDPN","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:fd1e575b625aba0ed16fd4380a0abca660604187505034ee5bbc9c2ee6a2b3ac","target":"graph","created_at":"2026-05-18T00:09:48Z","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":"Arrow's theorem implies that a social choice function satisfying Transitivity, the Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are allowed, a dictatorial social choice function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does n","authors_text":"Elchanan Mossel, Omer Tamuz","cross_cats":["econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-13T20:01:35Z","title":"Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2465","kind":"arxiv","version":2},"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":"sha256:3eb2c7f92cbbc795ff9a23be2f77bab978d26febd66f8d13943884ca192438f2","target":"record","created_at":"2026-05-18T00:09:48Z","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":"316bfd89ac4ef7abf14fa231a851715d993a1608615c97f8664f20d8013100bc","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-13T20:01:35Z","title_canon_sha256":"5dbfcaaa9ab6fe5f3b433370dccf424c0b2efed52d160a03fc57653cb2b4c7c6"},"schema_version":"1.0","source":{"id":"0910.2465","kind":"arxiv","version":2}},"canonical_sha256":"58b6458dedf5a2328abdea230a1bc3692fa7db039a39535c2491f1648c7ef726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58b6458dedf5a2328abdea230a1bc3692fa7db039a39535c2491f1648c7ef726","first_computed_at":"2026-05-18T00:09:48.290037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:48.290037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+9OclOIn6cFDDVdq8BpLMmAlrcvJ+ZoP/7/fTngfzbj8WKwz4iYgU4g0QrvAHisTthZUbij2uNvVOk7MQ4bmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:48.290844Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2465","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eb2c7f92cbbc795ff9a23be2f77bab978d26febd66f8d13943884ca192438f2","sha256:fd1e575b625aba0ed16fd4380a0abca660604187505034ee5bbc9c2ee6a2b3ac"],"state_sha256":"140afe619b990734fc4447393a254a1658a187c114ae2aa9320b8cadc9c6e75f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XeUTopP7HgsyMDtAOc9WNBTNSCua7s8Zy5BFGK33hZVbcNePCPM667fMMCiUG6oFWFYOP1UpzpnP7yDdxO90AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:08:43.116916Z","bundle_sha256":"8a5a519f7abcddeabdf814c15bd5dad6ae38711371e6f4874e42315661131316"}}