{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RIR2TR655WI6EO4KWYXFBWGDBX","short_pith_number":"pith:RIR2TR65","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"},"canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","source":{"kind":"arxiv","id":"2607.28298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28298","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28298v1","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28298","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_12","alias_value":"RIR2TR655WI6","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_16","alias_value":"RIR2TR655WI6EO4K","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_8","alias_value":"RIR2TR65","created_at":"2026-07-31T01:37:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RIR2TR655WI6EO4KWYXFBWGDBX","target":"record","payload":{"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"},"canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","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"},"source_kind":"arxiv","source_id":"2607.28298","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":"2026-07-31T01:37:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWBaorBN/S5A3y+UrjcBjXr8NFjTBQ+C/2fScPg9Gx31Vysu4UhlGaaH++BR+H4LVy4HfNgn2UwPhg/7bGwnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T01:19:24.575919Z"},"content_sha256":"8d952b5c78d44e9caea08b9dfd462c7c4a24c5feb312e7b4e72287d656030a75","schema_version":"1.0","event_id":"sha256:8d952b5c78d44e9caea08b9dfd462c7c4a24c5feb312e7b4e72287d656030a75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RIR2TR655WI6EO4KWYXFBWGDBX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-31T01:37:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2gg/1KkBDbsBG0IjZBulLidjCSl1wU8f/uYSn206pI9jzzP9ikPS4iZSqsTqMlXO7Oj9eX4eXKZxZM4WGTanDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T01:19:24.576448Z"},"content_sha256":"c6d6ab304914a0bfd1599d7d0c8d4fc4a7015fe499381042b4090740ce2c2c03","schema_version":"1.0","event_id":"sha256:c6d6ab304914a0bfd1599d7d0c8d4fc4a7015fe499381042b4090740ce2c2c03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/bundle.json","state_url":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIR2TR655WI6EO4KWYXFBWGDBX/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":"2026-08-03T01:19:24Z","links":{"resolver":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX","bundle":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/bundle.json","state":"https://pith.science/pith/RIR2TR655WI6EO4KWYXFBWGDBX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIR2TR655WI6EO4KWYXFBWGDBX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RIR2TR655WI6EO4KWYXFBWGDBX","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":"28ae15cabd092897b52c3973db67a53a95d19f4ce21d316ad61211b8cb3e470f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T14:39:52Z","title_canon_sha256":"85c5b5fdf360a2b15fb246978b2f3f41f41643fec3e9dfda5d88f0054fc15e06"},"schema_version":"1.0","source":{"id":"2607.28298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28298","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28298v1","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28298","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_12","alias_value":"RIR2TR655WI6","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_16","alias_value":"RIR2TR655WI6EO4K","created_at":"2026-07-31T01:37:10Z"},{"alias_kind":"pith_short_8","alias_value":"RIR2TR65","created_at":"2026-07-31T01:37:10Z"}],"graph_snapshots":[{"event_id":"sha256:c6d6ab304914a0bfd1599d7d0c8d4fc4a7015fe499381042b4090740ce2c2c03","target":"graph","created_at":"2026-07-31T01:37:10Z","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/2607.28298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 $A$ ","authors_text":"Heiko R\\\"oglin, Jan-Henrik Haunert, Joshua Marc K\\\"onen, Tarek Stuck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T14:39:52Z","title":"Finding Regions of Maximum Circularity in Plane Geometric Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28298","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":"sha256:8d952b5c78d44e9caea08b9dfd462c7c4a24c5feb312e7b4e72287d656030a75","target":"record","created_at":"2026-07-31T01:37:10Z","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":"28ae15cabd092897b52c3973db67a53a95d19f4ce21d316ad61211b8cb3e470f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T14:39:52Z","title_canon_sha256":"85c5b5fdf360a2b15fb246978b2f3f41f41643fec3e9dfda5d88f0054fc15e06"},"schema_version":"1.0","source":{"id":"2607.28298","kind":"arxiv","version":1}},"canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a23a9c7dded91e23b8ab62e50d8c30ddee06d6542b6f79ebe1cce83754e43c1","first_computed_at":"2026-07-31T01:37:10.536210Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:37:10.536210Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d952b5c78d44e9caea08b9dfd462c7c4a24c5feb312e7b4e72287d656030a75","sha256:c6d6ab304914a0bfd1599d7d0c8d4fc4a7015fe499381042b4090740ce2c2c03"],"state_sha256":"e33aef2e5362a093e54954bc1500fe6202f368b9bdfc09ec95d3ee31c4e184cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYrSgIcHIgGsvYB/NT6O4POOVgmP+Jf3uPG6b4TllqeOf2eyZS5QMkhE2lfNHOVcl/xqAALKE8Cmb0hzfjdTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T01:19:24.581547Z","bundle_sha256":"13164f9f5656b86bb15a51d5e4de14809074e551c08d291436ac13e91412de8e"}}