{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QOOCKHAWAJKXBLBIRA6V2LGSR7","short_pith_number":"pith:QOOCKHAW","canonical_record":{"source":{"id":"1710.11086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-10-30T17:32:54Z","cross_cats_sorted":[],"title_canon_sha256":"4bdc5e1115af9b67096164d8117169679b69ee23031d6803d3de8a92c7ee22c9","abstract_canon_sha256":"e331222e00d964b7151dd4231455a605c223baac2a2c2294c411c0d5f30d1319"},"schema_version":"1.0"},"canonical_sha256":"839c251c16025570ac28883d5d2cd28fd060516b6de61551aaef93538afb900f","source":{"kind":"arxiv","id":"1710.11086","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11086","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11086v2","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11086","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"QOOCKHAWAJKX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOOCKHAWAJKXBLBI","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOOCKHAW","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QOOCKHAWAJKXBLBIRA6V2LGSR7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.11086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-10-30T17:32:54Z","cross_cats_sorted":[],"title_canon_sha256":"4bdc5e1115af9b67096164d8117169679b69ee23031d6803d3de8a92c7ee22c9","abstract_canon_sha256":"e331222e00d964b7151dd4231455a605c223baac2a2c2294c411c0d5f30d1319"},"schema_version":"1.0"},"canonical_sha256":"839c251c16025570ac28883d5d2cd28fd060516b6de61551aaef93538afb900f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:40.323429Z","signature_b64":"ZJafROXaE9KFQIvlNZ9A7g2XROixjFxkGa6A3SXLZ3kdHIFgGQXTzVtjQOkVayolAbK4VZb35pSaaUviwiYQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"839c251c16025570ac28883d5d2cd28fd060516b6de61551aaef93538afb900f","last_reissued_at":"2026-05-18T00:30:40.322706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:40.322706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.11086","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":"2026-05-18T00:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XeAlTaJe0/0SIVeW/MQCTgRHOMoUtChf/viB3iTjCCvNHx4Br/gxxY0K+ClnHSUyVa40crep6BKJHh4F0i/lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:21:14.488379Z"},"content_sha256":"92247a072ef2bf081eb356d386b5d557f2c7be401526ae0fd1c22e78a5bf86f0","schema_version":"1.0","event_id":"sha256:92247a072ef2bf081eb356d386b5d557f2c7be401526ae0fd1c22e78a5bf86f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QOOCKHAWAJKXBLBIRA6V2LGSR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Relative Efficiency Gap formula for measuring Political Gerrymandering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Kristopher Tapp","submitted_at":"2017-10-30T17:32:54Z","abstract_excerpt":"The efficiency gap formula was introduced in to measure political gerrymandering. It played a key role in the Gill v. Whitford case whose appeal is currently before the Supreme Court, but it was very recently shown by Bernstein and Duchin to have some problematic mathematical properties. We propose a new relative version of the efficiency gap formula that inherits its desirable but not its undesirable features. Instead of measuring the difference between the number of votes wasted by the two parties, we measure the difference between the proportions of their votes that the two parties wasted."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11086","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":"2026-05-18T00:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CDfiHuBt0vgEgkMenywDBbBkMRIe/70D+b8U3L7dyo/OYVf9UXIQTk+X5VnlFUngvH98NW+9Cgy38YDIJ66iDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:21:14.488861Z"},"content_sha256":"f988b88dc52b22d8323ce53378a01f7fcd35408785bf6ca41dddf2317207a4a8","schema_version":"1.0","event_id":"sha256:f988b88dc52b22d8323ce53378a01f7fcd35408785bf6ca41dddf2317207a4a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/bundle.json","state_url":"https://pith.science/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/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":"2026-06-23T02:21:14Z","links":{"resolver":"https://pith.science/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7","bundle":"https://pith.science/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/bundle.json","state":"https://pith.science/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOOCKHAWAJKXBLBIRA6V2LGSR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QOOCKHAWAJKXBLBIRA6V2LGSR7","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":"e331222e00d964b7151dd4231455a605c223baac2a2c2294c411c0d5f30d1319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-10-30T17:32:54Z","title_canon_sha256":"4bdc5e1115af9b67096164d8117169679b69ee23031d6803d3de8a92c7ee22c9"},"schema_version":"1.0","source":{"id":"1710.11086","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11086","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11086v2","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11086","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"QOOCKHAWAJKX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOOCKHAWAJKXBLBI","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOOCKHAW","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:f988b88dc52b22d8323ce53378a01f7fcd35408785bf6ca41dddf2317207a4a8","target":"graph","created_at":"2026-05-18T00:30:40Z","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":"The efficiency gap formula was introduced in to measure political gerrymandering. It played a key role in the Gill v. Whitford case whose appeal is currently before the Supreme Court, but it was very recently shown by Bernstein and Duchin to have some problematic mathematical properties. We propose a new relative version of the efficiency gap formula that inherits its desirable but not its undesirable features. Instead of measuring the difference between the number of votes wasted by the two parties, we measure the difference between the proportions of their votes that the two parties wasted.","authors_text":"Kristopher Tapp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-10-30T17:32:54Z","title":"A Relative Efficiency Gap formula for measuring Political Gerrymandering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11086","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":"sha256:92247a072ef2bf081eb356d386b5d557f2c7be401526ae0fd1c22e78a5bf86f0","target":"record","created_at":"2026-05-18T00:30:40Z","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":"e331222e00d964b7151dd4231455a605c223baac2a2c2294c411c0d5f30d1319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-10-30T17:32:54Z","title_canon_sha256":"4bdc5e1115af9b67096164d8117169679b69ee23031d6803d3de8a92c7ee22c9"},"schema_version":"1.0","source":{"id":"1710.11086","kind":"arxiv","version":2}},"canonical_sha256":"839c251c16025570ac28883d5d2cd28fd060516b6de61551aaef93538afb900f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"839c251c16025570ac28883d5d2cd28fd060516b6de61551aaef93538afb900f","first_computed_at":"2026-05-18T00:30:40.322706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:40.322706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJafROXaE9KFQIvlNZ9A7g2XROixjFxkGa6A3SXLZ3kdHIFgGQXTzVtjQOkVayolAbK4VZb35pSaaUviwiYQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:40.323429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11086","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92247a072ef2bf081eb356d386b5d557f2c7be401526ae0fd1c22e78a5bf86f0","sha256:f988b88dc52b22d8323ce53378a01f7fcd35408785bf6ca41dddf2317207a4a8"],"state_sha256":"42d90e8e454fe215e038a942f5f00ef5750ed672404011569d772e56a306e6b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05GIqkwZJ78nvarLpmtzTVv4pxtsgwH8WS5BJMWfDOP7H33OMrdCz2c+cn8C2XULQoBREsagZ81WGflaPhG/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:21:14.491684Z","bundle_sha256":"5f4661442095c7ee26c1f015237fbd215e751a4d493ed4dbb2c6a1cfab0428ee"}}