{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PWBMCI3BVU74C3A27L6TFUCLSB","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":"e9673c9f72d25d46923acdb9c571a6b7e9d9c310b05ef33df1b465493353a465","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2024-07-12T15:43:03Z","title_canon_sha256":"a93537b9797faf2090c57014abc0ad462bfbf888a1258e61e15158e0b6c93b91"},"schema_version":"1.0","source":{"id":"2407.09362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.09362","created_at":"2026-07-05T10:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"2407.09362v2","created_at":"2026-07-05T10:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.09362","created_at":"2026-07-05T10:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"PWBMCI3BVU74","created_at":"2026-07-05T10:40:01Z"},{"alias_kind":"pith_short_16","alias_value":"PWBMCI3BVU74C3A2","created_at":"2026-07-05T10:40:01Z"},{"alias_kind":"pith_short_8","alias_value":"PWBMCI3B","created_at":"2026-07-05T10:40:01Z"}],"graph_snapshots":[{"event_id":"sha256:dc59274d1d9e7cd1863fc4f713d1842be4c5d8ce19a99a73b5a8d0f958b6731a","target":"graph","created_at":"2026-07-05T10:40:01Z","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/2407.09362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider intersection graphs of disks of radius $r$ in the hyperbolic plane. Unlike the Euclidean setting, these graph classes are different for different values of $r$, where very small $r$ corresponds to an almost-Euclidean setting and $r \\in \\Omega(\\log n)$ corresponds to a firmly hyperbolic setting. We observe that larger values of $r$ create simpler graph classes, at least in terms of separators and the computational complexity of the \\textsc{Independent Set} problem.\n  First, we show that intersection graphs of disks of radius $r$ in the hyperbolic plane can be separated with $\\mathca","authors_text":"Geert van Wordragen, Jean-Pierre von der Heydt, Marcus Wilhelm, S\\'andor Kisfaludi-Bak, Thomas Bl\\\"asius","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2024-07-12T15:43:03Z","title":"Structure and Independence in Hyperbolic Uniform Disk Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09362","kind":"arxiv","version":2},"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":"sha256:080f5c2f2b662ae9445c72285b7c0501b5280436590c80be9b14c23a36bc8d78","target":"record","created_at":"2026-07-05T10:40:01Z","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":"e9673c9f72d25d46923acdb9c571a6b7e9d9c310b05ef33df1b465493353a465","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2024-07-12T15:43:03Z","title_canon_sha256":"a93537b9797faf2090c57014abc0ad462bfbf888a1258e61e15158e0b6c93b91"},"schema_version":"1.0","source":{"id":"2407.09362","kind":"arxiv","version":2}},"canonical_sha256":"7d82c12361ad3fc16c1afafd32d04b90405e5f0f296fbfebfe77da541fadae8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d82c12361ad3fc16c1afafd32d04b90405e5f0f296fbfebfe77da541fadae8e","first_computed_at":"2026-07-05T10:40:01.831628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:01.831628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/mXad2nK/BxTuoWXSH9bI34jRIfisVLOjHjt9MqPk3aF6Uhap7WQOhs3KWIDG+R7JBs4sJMuohjt0r2Hn1rLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:01.832123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.09362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:080f5c2f2b662ae9445c72285b7c0501b5280436590c80be9b14c23a36bc8d78","sha256:dc59274d1d9e7cd1863fc4f713d1842be4c5d8ce19a99a73b5a8d0f958b6731a"],"state_sha256":"de1e09424519975e4d85536a91b53bd2892f578e97ebb166b6dfe88b6016f196"}