{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PWBMCI3BVU74C3A27L6TFUCLSB","short_pith_number":"pith:PWBMCI3B","canonical_record":{"source":{"id":"2407.09362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2024-07-12T15:43:03Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"a93537b9797faf2090c57014abc0ad462bfbf888a1258e61e15158e0b6c93b91","abstract_canon_sha256":"e9673c9f72d25d46923acdb9c571a6b7e9d9c310b05ef33df1b465493353a465"},"schema_version":"1.0"},"canonical_sha256":"7d82c12361ad3fc16c1afafd32d04b90405e5f0f296fbfebfe77da541fadae8e","source":{"kind":"arxiv","id":"2407.09362","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PWBMCI3BVU74C3A27L6TFUCLSB","target":"record","payload":{"canonical_record":{"source":{"id":"2407.09362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2024-07-12T15:43:03Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"a93537b9797faf2090c57014abc0ad462bfbf888a1258e61e15158e0b6c93b91","abstract_canon_sha256":"e9673c9f72d25d46923acdb9c571a6b7e9d9c310b05ef33df1b465493353a465"},"schema_version":"1.0"},"canonical_sha256":"7d82c12361ad3fc16c1afafd32d04b90405e5f0f296fbfebfe77da541fadae8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:01.832123Z","signature_b64":"/mXad2nK/BxTuoWXSH9bI34jRIfisVLOjHjt9MqPk3aF6Uhap7WQOhs3KWIDG+R7JBs4sJMuohjt0r2Hn1rLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d82c12361ad3fc16c1afafd32d04b90405e5f0f296fbfebfe77da541fadae8e","last_reissued_at":"2026-07-05T10:40:01.831628Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:01.831628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.09362","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Kg9SNel6uXVqVTMX6isc/LVuiPhjwiLOJgU/ZzHFMpqm+IS9GDYvu8Z7GGPHz8vV79MGCWpt6U3lipms3INCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:54:18.732087Z"},"content_sha256":"080f5c2f2b662ae9445c72285b7c0501b5280436590c80be9b14c23a36bc8d78","schema_version":"1.0","event_id":"sha256:080f5c2f2b662ae9445c72285b7c0501b5280436590c80be9b14c23a36bc8d78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PWBMCI3BVU74C3A27L6TFUCLSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure and Independence in Hyperbolic Uniform Disk Graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Geert van Wordragen, Jean-Pierre von der Heydt, Marcus Wilhelm, S\\'andor Kisfaludi-Bak, Thomas Bl\\\"asius","submitted_at":"2024-07-12T15:43:03Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09362","kind":"arxiv","version":2},"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/2407.09362/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":"2026-07-05T10:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OIHCXcgixousFtTTHhDgJrdRTZ7cng3klHwfLun6kUfP4dvIs/JmR7ZflDsUtmo74J4WcteWGZJJqLhMVuciAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:54:18.732588Z"},"content_sha256":"dc59274d1d9e7cd1863fc4f713d1842be4c5d8ce19a99a73b5a8d0f958b6731a","schema_version":"1.0","event_id":"sha256:dc59274d1d9e7cd1863fc4f713d1842be4c5d8ce19a99a73b5a8d0f958b6731a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWBMCI3BVU74C3A27L6TFUCLSB/bundle.json","state_url":"https://pith.science/pith/PWBMCI3BVU74C3A27L6TFUCLSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWBMCI3BVU74C3A27L6TFUCLSB/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":"2026-08-15T11:54:18Z","links":{"resolver":"https://pith.science/pith/PWBMCI3BVU74C3A27L6TFUCLSB","bundle":"https://pith.science/pith/PWBMCI3BVU74C3A27L6TFUCLSB/bundle.json","state":"https://pith.science/pith/PWBMCI3BVU74C3A27L6TFUCLSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWBMCI3BVU74C3A27L6TFUCLSB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEOcIF/RKCPjnlEReEccjPPyXhyK4bkkRXqf0j4sRX10QcdjdzXdaLOBlQJ7OynZqD8vIDUL/DfPIGmlknd9Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T11:54:18.736443Z","bundle_sha256":"8ddb7fba12d6117583881af581c3c5d07acace70fffb845deefa61c117c2f798"}}