{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:66SOV64J5MXTS6DJPWKNT5LZFQ","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":"e20f4a6aadec65ddc5bbf1fe235e51e18b38062be3e7d260e83c669313162e35","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-18T17:34:55Z","title_canon_sha256":"4ef21a6af7ab6d3cdb83e4ec88f51fdcf8d8b95a51dd7f5d3d0df1cf530a265a"},"schema_version":"1.0","source":{"id":"2008.08054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.08054","created_at":"2026-07-05T01:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"2008.08054v1","created_at":"2026-07-05T01:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.08054","created_at":"2026-07-05T01:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"66SOV64J5MXT","created_at":"2026-07-05T01:27:58Z"},{"alias_kind":"pith_short_16","alias_value":"66SOV64J5MXTS6DJ","created_at":"2026-07-05T01:27:58Z"},{"alias_kind":"pith_short_8","alias_value":"66SOV64J","created_at":"2026-07-05T01:27:58Z"}],"graph_snapshots":[{"event_id":"sha256:df89b81be4e726b831b0a96740785d046de9266aef63060b76a59e89d66f46a6","target":"graph","created_at":"2026-07-05T01:27:58Z","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/2008.08054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a partition with a specified number of elements which each correspond to a different district. The districts satisfy a collection of hard constraints and the measure may be weighted with regard to a number of other criteria. The multi-scale algorithm is similar to our previously developed Merge-Split proposal, however, this algorithm provides improved scaling prop","authors_text":"Daniel Carter, Eric A. Autry, Gregory Herschlag, Jonathan C. Mattingly, Zach Hunter","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-18T17:34:55Z","title":"Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.08054","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":"sha256:762aa71d5ab1a4bc382c42212cf52ff710f9a4e11a660896206f55fe3325522a","target":"record","created_at":"2026-07-05T01:27:58Z","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":"e20f4a6aadec65ddc5bbf1fe235e51e18b38062be3e7d260e83c669313162e35","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-18T17:34:55Z","title_canon_sha256":"4ef21a6af7ab6d3cdb83e4ec88f51fdcf8d8b95a51dd7f5d3d0df1cf530a265a"},"schema_version":"1.0","source":{"id":"2008.08054","kind":"arxiv","version":1}},"canonical_sha256":"f7a4eafb89eb2f3978697d94d9f5792c13966f7895b100cad6233ae8230d1929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7a4eafb89eb2f3978697d94d9f5792c13966f7895b100cad6233ae8230d1929","first_computed_at":"2026-07-05T01:27:58.315398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:27:58.315398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59u9dfx5dx1jhdHUQshKGyY48QEe/TGTdyLkEXXGNT9MyxnsCKPg6Bod7hma0MyN9qtY+OJ1t+ENpLN/YT7mAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:27:58.315851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.08054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:762aa71d5ab1a4bc382c42212cf52ff710f9a4e11a660896206f55fe3325522a","sha256:df89b81be4e726b831b0a96740785d046de9266aef63060b76a59e89d66f46a6"],"state_sha256":"cba46c5d863624110b98c929d908d22cf748a2e31e12cc405276e0c67d97a66d"}