{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4DYDDPXPQV2S4J4R2FXKPX23UK","short_pith_number":"pith:4DYDDPXP","schema_version":"1.0","canonical_sha256":"e0f031beef85752e2791d16ea7df5ba2831a4e4ec89e598191126a3b8cdadfd4","source":{"kind":"arxiv","id":"2606.10152","version":1},"attestation_state":"computed","paper":{"title":"Connectivity of Districting Metagraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel C. Jerison, Ellen Veomett, Mehmet Emre","submitted_at":"2026-06-08T20:31:10Z","abstract_excerpt":"In this article, we prove irreducibility results for a family of Markov chains arising in the study of redistricting and detecting gerrymandering. These chains use ReCom moves as their transition mechanism and are commonly employed in Markov chain Monte Carlo methods to generate ensembles of districting plans. Such ensembles are frequently used for outlier analysis, in which a proposed districting map is compared against the ensemble to determine whether it behaves atypically; this methodology often appears in expert testimony in redistricting litigation.\n  We show that when the underlying dua"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.10152","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-08T20:31:10Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"6acaa3b4d337931af07015aa087eebf0533bb861a33ab6db406314f905855bfd","abstract_canon_sha256":"6dd20ef4e7d4db6747491ce9db625b4be348d432bf99c1e56a2f30239a628562"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:08:56.872588Z","signature_b64":"Aqd5V+0s5yYHpM7Ga4pCngyh57cBkwu9L0tzpV+HTSrOCZiROJdxpTsNzBA9DYY7A1EejMvtO6zoXIpmOT9TBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f031beef85752e2791d16ea7df5ba2831a4e4ec89e598191126a3b8cdadfd4","last_reissued_at":"2026-06-10T01:08:56.871734Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:08:56.871734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity of Districting Metagraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel C. Jerison, Ellen Veomett, Mehmet Emre","submitted_at":"2026-06-08T20:31:10Z","abstract_excerpt":"In this article, we prove irreducibility results for a family of Markov chains arising in the study of redistricting and detecting gerrymandering. These chains use ReCom moves as their transition mechanism and are commonly employed in Markov chain Monte Carlo methods to generate ensembles of districting plans. Such ensembles are frequently used for outlier analysis, in which a proposed districting map is compared against the ensemble to determine whether it behaves atypically; this methodology often appears in expert testimony in redistricting litigation.\n  We show that when the underlying dua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10152/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.10152","created_at":"2026-06-10T01:08:56.871880+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10152v1","created_at":"2026-06-10T01:08:56.871880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10152","created_at":"2026-06-10T01:08:56.871880+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DYDDPXPQV2S","created_at":"2026-06-10T01:08:56.871880+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DYDDPXPQV2S4J4R","created_at":"2026-06-10T01:08:56.871880+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DYDDPXP","created_at":"2026-06-10T01:08:56.871880+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK","json":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK.json","graph_json":"https://pith.science/api/pith-number/4DYDDPXPQV2S4J4R2FXKPX23UK/graph.json","events_json":"https://pith.science/api/pith-number/4DYDDPXPQV2S4J4R2FXKPX23UK/events.json","paper":"https://pith.science/paper/4DYDDPXP"},"agent_actions":{"view_html":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK","download_json":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK.json","view_paper":"https://pith.science/paper/4DYDDPXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10152&json=true","fetch_graph":"https://pith.science/api/pith-number/4DYDDPXPQV2S4J4R2FXKPX23UK/graph.json","fetch_events":"https://pith.science/api/pith-number/4DYDDPXPQV2S4J4R2FXKPX23UK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK/action/storage_attestation","attest_author":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK/action/author_attestation","sign_citation":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK/action/citation_signature","submit_replication":"https://pith.science/pith/4DYDDPXPQV2S4J4R2FXKPX23UK/action/replication_record"}},"created_at":"2026-06-10T01:08:56.871880+00:00","updated_at":"2026-06-10T01:08:56.871880+00:00"}