{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VE7J6EDU3AMDSDDY5QHOYM7IA5","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":"194fa7f4245eac9b437eb987686ef3faa8bba55ad300e605d684d363869374be","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-19T11:37:17Z","title_canon_sha256":"8c9b006bed9146d299beeecb93241b7bd9189656f37a7a16b5b93c9607aef146"},"schema_version":"1.0","source":{"id":"1308.3987","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3987","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3987v3","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3987","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"VE7J6EDU3AMD","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VE7J6EDU3AMDSDDY","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VE7J6EDU","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:4aae63f07aaed9b4ae1dd174d0dcda0195a2dd1f9ca0519968690ae000c1f809","target":"graph","created_at":"2026-05-17T23:58:42Z","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"},"paper":{"abstract_excerpt":"In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s' with s'<s, are \\delta-hyperbolic with \\delta=O(s^2). We also show that the dependency between \\delta and s is linear if s-s'=\\Omega(s) and G obeys a slightly stronger condition. This solves an open question from the paper (J. Chalopin et al., Cop and robber games when the robber can hide and ride, SIAM J. Discr. Math. 25 (2011) 333-359). Since any \\delta-hyperbolic graph is cop-win for s=2r and s'=r+2\\delta for any r>0, this establishes a new - game-theoretical - chara","authors_text":"J\\'er\\'emie Chalopin, Panos Papasoglu, Timoth\\'ee Pecatte, Victor Chepoi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-19T11:37:17Z","title":"Cop and robber game and hyperbolicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3987","kind":"arxiv","version":3},"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":"sha256:1b743373b84b97e22d62132fc9f37a858943104ecc69af370401240c8232a51f","target":"record","created_at":"2026-05-17T23:58:42Z","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":"194fa7f4245eac9b437eb987686ef3faa8bba55ad300e605d684d363869374be","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-19T11:37:17Z","title_canon_sha256":"8c9b006bed9146d299beeecb93241b7bd9189656f37a7a16b5b93c9607aef146"},"schema_version":"1.0","source":{"id":"1308.3987","kind":"arxiv","version":3}},"canonical_sha256":"a93e9f1074d818390c78ec0eec33e8074a5b6596482457584f4cfb5daf67ff1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a93e9f1074d818390c78ec0eec33e8074a5b6596482457584f4cfb5daf67ff1b","first_computed_at":"2026-05-17T23:58:42.775582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:42.775582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dUKYR1C+tTEmiUSq8j+D3xKfnZ2KOqzLGUgfWSCA5BQYJUz7ZS70ZvTsjTSnL7MKCvuhHBYOQ7Up2KhXthcWCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:42.776310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3987","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b743373b84b97e22d62132fc9f37a858943104ecc69af370401240c8232a51f","sha256:4aae63f07aaed9b4ae1dd174d0dcda0195a2dd1f9ca0519968690ae000c1f809"],"state_sha256":"ad8218e9ae2b07255be08745fe4bcc2da8fa9171ad8e5497c6c8769c975985a6"}