{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6KAPFXZMDZBJJ4XTSMRRPG726X","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":"4875e9cc2537623179f54379b932eb991aa19e8261f40471258eda56eb85f752","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-09T07:43:32Z","title_canon_sha256":"14ff6e8b4d914e062ed85cf36e41ac3c95efe2269a98bb87c00e2516f83f9fea"},"schema_version":"1.0","source":{"id":"2603.08052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.08052","created_at":"2026-06-24T01:15:01Z"},{"alias_kind":"arxiv_version","alias_value":"2603.08052v2","created_at":"2026-06-24T01:15:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.08052","created_at":"2026-06-24T01:15:01Z"},{"alias_kind":"pith_short_12","alias_value":"6KAPFXZMDZBJ","created_at":"2026-06-24T01:15:01Z"},{"alias_kind":"pith_short_16","alias_value":"6KAPFXZMDZBJJ4XT","created_at":"2026-06-24T01:15:01Z"},{"alias_kind":"pith_short_8","alias_value":"6KAPFXZM","created_at":"2026-06-24T01:15:01Z"}],"graph_snapshots":[{"event_id":"sha256:3b0cc00d2e11856c452c19f7f5a90b2c4a7ed1092d880024770299d69c916565","target":"graph","created_at":"2026-06-24T01:15:01Z","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/2603.08052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a variant of the classical Cops and Robbers game with one cop and one robber. The cop follows a fixed walk on the graph, called a patrol, that is chosen before the game begins. The robber is omniscient and knows the entire patrol in advance. A capture occurs when the robber comes within a given distance of the cop, and this distance is referred to as the capture distance.\n  The patrol capture radius, $\\tilde{\\rho}{(G)}$, is the minimum radius of capture required for the cop to always be able to capture the robber on a connected graph $G$, under optimal play. We initiate a systematic s","authors_text":"Andrej Taranenko, Milo\\v{s} Stojakovi\\'c, Nina Chiarelli, Paul Dorbec","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-09T07:43:32Z","title":"Patrolling cop vs omniscient robber"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.08052","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:c020b192ea6511529a341eeed8c4558ee50a1ca6a0b306506a77c3b9183da6e2","target":"record","created_at":"2026-06-24T01:15:01Z","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":"4875e9cc2537623179f54379b932eb991aa19e8261f40471258eda56eb85f752","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-09T07:43:32Z","title_canon_sha256":"14ff6e8b4d914e062ed85cf36e41ac3c95efe2269a98bb87c00e2516f83f9fea"},"schema_version":"1.0","source":{"id":"2603.08052","kind":"arxiv","version":2}},"canonical_sha256":"f280f2df2c1e4294f2f39323179bfaf5c4f98001e485efd0c55310886f0136a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f280f2df2c1e4294f2f39323179bfaf5c4f98001e485efd0c55310886f0136a5","first_computed_at":"2026-06-24T01:15:01.625032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:01.625032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ybaNRnWefmCPhGt6hq3O+sCWfllwZXxVV9GVaNAWsYdwKQzrhdu6OHTVnPErdeGUVTj32V4/QqJ1KcGEXLPPDQ==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:01.625460Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.08052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c020b192ea6511529a341eeed8c4558ee50a1ca6a0b306506a77c3b9183da6e2","sha256:3b0cc00d2e11856c452c19f7f5a90b2c4a7ed1092d880024770299d69c916565"],"state_sha256":"176265fec9ddcd0bc5cc973a0e1544c15702d0989e5cd435097f32ea10ea5d88"}