{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IDC3HO435ZULSTVF4D62TG6VR7","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":"b9c58e3c4935709d6688ec75ca77b8d812a3ad8055767fcc8aaa03903494c702","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2025-05-21T12:00:32Z","title_canon_sha256":"aeae45c229460014a79011e47dedbe50c96688a756012e979318c452779b2bf8"},"schema_version":"1.0","source":{"id":"2505.15416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.15416","created_at":"2026-07-05T11:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"2505.15416v1","created_at":"2026-07-05T11:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.15416","created_at":"2026-07-05T11:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"IDC3HO435ZUL","created_at":"2026-07-05T11:06:45Z"},{"alias_kind":"pith_short_16","alias_value":"IDC3HO435ZULSTVF","created_at":"2026-07-05T11:06:45Z"},{"alias_kind":"pith_short_8","alias_value":"IDC3HO43","created_at":"2026-07-05T11:06:45Z"}],"graph_snapshots":[{"event_id":"sha256:07c13cff1ef973cc9b8c75e52bea94dfe55792baf486beeb0d543ecb3e0f133c","target":"graph","created_at":"2026-07-05T11:06:45Z","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/2505.15416/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The game of cops and robber is a two-player turn-based game played on a graph where the cops try to capture the robber. The cop number of a graph $G$, denoted by $c(G)$ is the minimum number of cops required to capture the robber. For a given class of graphs ${\\cal F}$, let $c({\\cal F}):=\\sup\\{c(F)|F\\in {\\cal F}\\}$, and let Forb$({\\cal F})$ denote the class of ${\\cal F}$-free graphs. We show that the complement of the Shrikhande graph is $(4K_1,C_{\\ell}$)-free for any $\\ell \\geq 6$ and has the cop number~$3$. This provides a counterexample for the conjecture proposed by Sivaraman (arxiv, 2019)","authors_text":"Arnab Char, Dinabandhu Pradhan, Paras Vinubhai Maniya","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2025-05-21T12:00:32Z","title":"$4K_1$-free graph with the cop number $3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15416","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:a6c74a3b6734c95e23832ee350d4335ac8e63a21cb07211d4a1f6006d1f403a2","target":"record","created_at":"2026-07-05T11:06:45Z","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":"b9c58e3c4935709d6688ec75ca77b8d812a3ad8055767fcc8aaa03903494c702","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2025-05-21T12:00:32Z","title_canon_sha256":"aeae45c229460014a79011e47dedbe50c96688a756012e979318c452779b2bf8"},"schema_version":"1.0","source":{"id":"2505.15416","kind":"arxiv","version":1}},"canonical_sha256":"40c5b3bb9bee68b94ea5e0fda99bd58feb3be7cc20171ecd76e0a3ea363b5405","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c5b3bb9bee68b94ea5e0fda99bd58feb3be7cc20171ecd76e0a3ea363b5405","first_computed_at":"2026-07-05T11:06:45.225598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:45.225598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0zmx1GfLgXrlwQJ0F7HwX5vL6Xv87GnsvUbl66TGcAPjwQoDelt/QwbBQp/RT+wgyu94Np2c7cj1uKQc77dAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:45.226071Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.15416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6c74a3b6734c95e23832ee350d4335ac8e63a21cb07211d4a1f6006d1f403a2","sha256:07c13cff1ef973cc9b8c75e52bea94dfe55792baf486beeb0d543ecb3e0f133c"],"state_sha256":"815d5b02e236c668f6b40df81b472486ac8c78c95f4a5b5149a4793f9ba2b5a7"}