{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RIR2TR655WI6EO4KWYXFBWGDBX","short_pith_number":"pith:RIR2TR65","schema_version":"1.0","canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","source":{"kind":"arxiv","id":"2607.28298","version":1},"attestation_state":"computed","paper":{"title":"Finding Regions of Maximum Circularity in Plane Geometric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Heiko R\\\"oglin, Jan-Henrik Haunert, Joshua Marc K\\\"onen, Tarek Stuck","submitted_at":"2026-07-30T14:39:52Z","abstract_excerpt":"A problem that occurs in different applications in geographical information science is to generate compact regions from areas on a map. This is important, e.g., in the context of electoral districting to avoid gerrymandering. A common measure for the compactness of a region is the Polsby-Popper score, which measures how close a given region is to a circle based on its area and perimeter. We assume that a polygonal subdivision of the plane is given and study the problem of selecting a subset of the polygonal faces that maximizes the Polsby-Popper score, given by $\\frac{4\\pi A}{P^2}$, where $A$ "},"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":"2607.28298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T14:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"85c5b5fdf360a2b15fb246978b2f3f41f41643fec3e9dfda5d88f0054fc15e06","abstract_canon_sha256":"28ae15cabd092897b52c3973db67a53a95d19f4ce21d316ad61211b8cb3e470f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","last_reissued_at":"2026-07-31T01:37:10.536210Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:37:10.536210Z"},"graph_snapshot":{"paper":{"title":"Finding Regions of Maximum Circularity in Plane Geometric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Heiko R\\\"oglin, Jan-Henrik Haunert, Joshua Marc K\\\"onen, Tarek Stuck","submitted_at":"2026-07-30T14:39:52Z","abstract_excerpt":"A problem that occurs in different applications in geographical information science is to generate compact regions from areas on a map. This is important, e.g., in the context of electoral districting to avoid gerrymandering. A common measure for the compactness of a region is the Polsby-Popper score, which measures how close a given region is to a circle based on its area and perimeter. We assume that a polygonal subdivision of the plane is given and study the problem of selecting a subset of the polygonal faces that maximizes the Polsby-Popper score, given by $\\frac{4\\pi A}{P^2}$, where $A$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28298","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/2607.28298/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":"2607.28298","created_at":"2026-07-31T01:37:10.539446+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28298v1","created_at":"2026-07-31T01:37:10.539446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28298","created_at":"2026-07-31T01:37:10.539446+00:00"},{"alias_kind":"pith_short_12","alias_value":"RIR2TR655WI6","created_at":"2026-07-31T01:37:10.539446+00:00"},{"alias_kind":"pith_short_16","alias_value":"RIR2TR655WI6EO4K","created_at":"2026-07-31T01:37:10.539446+00:00"},{"alias_kind":"pith_short_8","alias_value":"RIR2TR65","created_at":"2026-07-31T01:37:10.539446+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/RIR2TR655WI6EO4KWYXFBWGDBX","json":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX.json","graph_json":"https://pith.science/api/pith-number/RIR2TR655WI6EO4KWYXFBWGDBX/graph.json","events_json":"https://pith.science/api/pith-number/RIR2TR655WI6EO4KWYXFBWGDBX/events.json","paper":"https://pith.science/paper/RIR2TR65"},"agent_actions":{"view_html":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX","download_json":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX.json","view_paper":"https://pith.science/paper/RIR2TR65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28298&json=true","fetch_graph":"https://pith.science/api/pith-number/RIR2TR655WI6EO4KWYXFBWGDBX/graph.json","fetch_events":"https://pith.science/api/pith-number/RIR2TR655WI6EO4KWYXFBWGDBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/action/storage_attestation","attest_author":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/action/author_attestation","sign_citation":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/action/citation_signature","submit_replication":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/action/replication_record"}},"created_at":"2026-07-31T01:37:10.539446+00:00","updated_at":"2026-07-31T01:37:10.539446+00:00"}