{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OJXG6DBGSR6OIRU47CF6NP4MPI","short_pith_number":"pith:OJXG6DBG","canonical_record":{"source":{"id":"1805.08208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-05-20T02:21:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"dc8058ee39969290f34f69e5d20f5847db9740665f8859030de210e64cbf9194","abstract_canon_sha256":"c9357770ddf65702b465afdfe0593f9503e7cc0c3092287db745ca754df6a111"},"schema_version":"1.0"},"canonical_sha256":"726e6f0c26947ce4469cf88be6bf8c7a03b8ce33a74b4849e3f2181c5ed67b1f","source":{"kind":"arxiv","id":"1805.08208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08208","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08208v1","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08208","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"OJXG6DBGSR6O","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OJXG6DBGSR6OIRU4","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OJXG6DBG","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OJXG6DBGSR6OIRU47CF6NP4MPI","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-05-20T02:21:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"dc8058ee39969290f34f69e5d20f5847db9740665f8859030de210e64cbf9194","abstract_canon_sha256":"c9357770ddf65702b465afdfe0593f9503e7cc0c3092287db745ca754df6a111"},"schema_version":"1.0"},"canonical_sha256":"726e6f0c26947ce4469cf88be6bf8c7a03b8ce33a74b4849e3f2181c5ed67b1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:27.243520Z","signature_b64":"imHwJqyqaBmeq44kojUKvrZPGBrRhJzr2DseVt4N3A4m97/Lq1DxTsp97GGX6/TVuTKff8dyg00GDMk7GNPCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"726e6f0c26947ce4469cf88be6bf8c7a03b8ce33a74b4849e3f2181c5ed67b1f","last_reissued_at":"2026-05-18T00:15:27.242746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:27.242746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08208","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":"2026-05-18T00:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnLzrTvPP0kyMB07w4ILwQAiTCc9IJBDe2fYeCeFeqyvNgu2imMkccsoUokTkMmTsBFR/258KPmWh5rYlsZBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:53:25.606978Z"},"content_sha256":"115c0e766501f19410e4b3f615482d8a33b8de1e99f8780552c1175a11dd7e23","schema_version":"1.0","event_id":"sha256:115c0e766501f19410e4b3f615482d8a33b8de1e99f8780552c1175a11dd7e23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OJXG6DBGSR6OIRU47CF6NP4MPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measuring Congressional District Meandering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.HO","authors_text":"Eion Blanchard, Kevin Knudson","submitted_at":"2018-05-20T02:21:07Z","abstract_excerpt":"In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts \"meander\" via a computation of the medial axis of the region. We then compare this to the medial axis of the convex hull of the district to obtain the {\\em medial-hull ratio}: a dimensionless quantity that captures the district's irregularity. We compute this quantity for many example Congressional districts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08208","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":"2026-05-18T00:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDpAXyTDn6IJN+R7w1LjNk2xZuQOVWXEyxMT2y7naM4j4t7icpDk3t5qzDqbN0lZZhaVRqsp1eqbag56yWyiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:53:25.607334Z"},"content_sha256":"2d00d04c0eeef380a6fe7defde5e13f4993e1944c22b577302676c83366ac93f","schema_version":"1.0","event_id":"sha256:2d00d04c0eeef380a6fe7defde5e13f4993e1944c22b577302676c83366ac93f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/bundle.json","state_url":"https://pith.science/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/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":"2026-06-23T03:53:25Z","links":{"resolver":"https://pith.science/pith/OJXG6DBGSR6OIRU47CF6NP4MPI","bundle":"https://pith.science/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/bundle.json","state":"https://pith.science/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJXG6DBGSR6OIRU47CF6NP4MPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OJXG6DBGSR6OIRU47CF6NP4MPI","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":"c9357770ddf65702b465afdfe0593f9503e7cc0c3092287db745ca754df6a111","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-05-20T02:21:07Z","title_canon_sha256":"dc8058ee39969290f34f69e5d20f5847db9740665f8859030de210e64cbf9194"},"schema_version":"1.0","source":{"id":"1805.08208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08208","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08208v1","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08208","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"OJXG6DBGSR6O","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OJXG6DBGSR6OIRU4","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OJXG6DBG","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:2d00d04c0eeef380a6fe7defde5e13f4993e1944c22b577302676c83366ac93f","target":"graph","created_at":"2026-05-18T00:15:27Z","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":"In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts \"meander\" via a computation of the medial axis of the region. We then compare this to the medial axis of the convex hull of the district to obtain the {\\em medial-hull ratio}: a dimensionless quantity that captures the district's irregularity. We compute this quantity for many example Congressional districts.","authors_text":"Eion Blanchard, Kevin Knudson","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-05-20T02:21:07Z","title":"Measuring Congressional District Meandering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08208","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":"sha256:115c0e766501f19410e4b3f615482d8a33b8de1e99f8780552c1175a11dd7e23","target":"record","created_at":"2026-05-18T00:15:27Z","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":"c9357770ddf65702b465afdfe0593f9503e7cc0c3092287db745ca754df6a111","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-05-20T02:21:07Z","title_canon_sha256":"dc8058ee39969290f34f69e5d20f5847db9740665f8859030de210e64cbf9194"},"schema_version":"1.0","source":{"id":"1805.08208","kind":"arxiv","version":1}},"canonical_sha256":"726e6f0c26947ce4469cf88be6bf8c7a03b8ce33a74b4849e3f2181c5ed67b1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"726e6f0c26947ce4469cf88be6bf8c7a03b8ce33a74b4849e3f2181c5ed67b1f","first_computed_at":"2026-05-18T00:15:27.242746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:27.242746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"imHwJqyqaBmeq44kojUKvrZPGBrRhJzr2DseVt4N3A4m97/Lq1DxTsp97GGX6/TVuTKff8dyg00GDMk7GNPCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:27.243520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:115c0e766501f19410e4b3f615482d8a33b8de1e99f8780552c1175a11dd7e23","sha256:2d00d04c0eeef380a6fe7defde5e13f4993e1944c22b577302676c83366ac93f"],"state_sha256":"7df6638e262776b185502823629897f0ee0d6ca3dbc042eb65733e693a3dc76a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEEEiYv1em7USTnLfs+/VqaDri+Nv9c9UOxDxFZ74BTuHgoPG3Qlu8D2HSji47xIEihuxxy5RbSWQBBqxU6TCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:53:25.609380Z","bundle_sha256":"4d9cc56727ff6891b1a0ab0d9210e96a037a151f41cf88e5844e2891b73dd9bc"}}