{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EBKSBSKMW7IEBESXBMIJMQQQ5X","short_pith_number":"pith:EBKSBSKM","canonical_record":{"source":{"id":"2112.07449","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-12-14T15:07:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"313c949689b0286331ac911f725704b994eca46f23aca4e67d3d429e982d5355","abstract_canon_sha256":"e1c8feb4e1c5cbc1025e5a2f6ed099a059df090dd28adef89f30bdefac3f1f83"},"schema_version":"1.0"},"canonical_sha256":"205520c94cb7d04092570b10964210edebe1dbb52ec958ff01fa4399a3ee70e0","source":{"kind":"arxiv","id":"2112.07449","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.07449","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"2112.07449v2","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.07449","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"EBKSBSKMW7IE","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_16","alias_value":"EBKSBSKMW7IEBESX","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_8","alias_value":"EBKSBSKM","created_at":"2026-07-05T04:31:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EBKSBSKMW7IEBESXBMIJMQQQ5X","target":"record","payload":{"canonical_record":{"source":{"id":"2112.07449","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-12-14T15:07:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"313c949689b0286331ac911f725704b994eca46f23aca4e67d3d429e982d5355","abstract_canon_sha256":"e1c8feb4e1c5cbc1025e5a2f6ed099a059df090dd28adef89f30bdefac3f1f83"},"schema_version":"1.0"},"canonical_sha256":"205520c94cb7d04092570b10964210edebe1dbb52ec958ff01fa4399a3ee70e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:31:58.373706Z","signature_b64":"xQnh96gmjZpUJlvVKpFsWuX5APjGxxl9QvNHZg8uWDN4tLzZAf88P9WsWwYiRbwuHFgrAUFjVmL/zJI/ZpQZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"205520c94cb7d04092570b10964210edebe1dbb52ec958ff01fa4399a3ee70e0","last_reissued_at":"2026-07-05T04:31:58.373147Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:31:58.373147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.07449","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":"2026-07-05T04:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"anvngUUcrMsdW/BKaIIQ2a7nKbZyo5dcf+d1fi9HvaNjAoyUgTbYbYM27TjPvaKZHd+UbUrlyaS6J7nKNePuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T10:05:53.710259Z"},"content_sha256":"21a8000c84226e1b6342e8436d9337146412e72a56cd306fd8f2ee57afebf99d","schema_version":"1.0","event_id":"sha256:21a8000c84226e1b6342e8436d9337146412e72a56cd306fd8f2ee57afebf99d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EBKSBSKMW7IEBESXBMIJMQQQ5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A faster algorithm for Cops and Robbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Jan Petr, Julien Portier, Leo Versteegen","submitted_at":"2021-12-14T15:07:08Z","abstract_excerpt":"We present an algorithm of time complexity $O(kn^{k+2})$ deciding whether a graph $G$ on $n$ vertices is $k$-copwin. The fastest algorithm thus far had time complexity $O(n^{2k+2})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07449","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/2112.07449/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":"2026-07-05T04:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjbKddRtVHEsrMFBb+D+Q+ypw/2WSq88gJUlcmsov6YJtc5FW5QCp6a/aX0zCJTT03b+qNe5rlIp3smV6ZDOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T10:05:53.710643Z"},"content_sha256":"377072c725657f79f5be88da06416834e24788f5ca222969ae6ca47f34ac5f30","schema_version":"1.0","event_id":"sha256:377072c725657f79f5be88da06416834e24788f5ca222969ae6ca47f34ac5f30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/bundle.json","state_url":"https://pith.science/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/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":"2026-07-17T10:05:53Z","links":{"resolver":"https://pith.science/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X","bundle":"https://pith.science/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/bundle.json","state":"https://pith.science/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBKSBSKMW7IEBESXBMIJMQQQ5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EBKSBSKMW7IEBESXBMIJMQQQ5X","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":"e1c8feb4e1c5cbc1025e5a2f6ed099a059df090dd28adef89f30bdefac3f1f83","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-12-14T15:07:08Z","title_canon_sha256":"313c949689b0286331ac911f725704b994eca46f23aca4e67d3d429e982d5355"},"schema_version":"1.0","source":{"id":"2112.07449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.07449","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"2112.07449v2","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.07449","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"EBKSBSKMW7IE","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_16","alias_value":"EBKSBSKMW7IEBESX","created_at":"2026-07-05T04:31:58Z"},{"alias_kind":"pith_short_8","alias_value":"EBKSBSKM","created_at":"2026-07-05T04:31:58Z"}],"graph_snapshots":[{"event_id":"sha256:377072c725657f79f5be88da06416834e24788f5ca222969ae6ca47f34ac5f30","target":"graph","created_at":"2026-07-05T04:31:58Z","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/2112.07449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an algorithm of time complexity $O(kn^{k+2})$ deciding whether a graph $G$ on $n$ vertices is $k$-copwin. The fastest algorithm thus far had time complexity $O(n^{2k+2})$.","authors_text":"Jan Petr, Julien Portier, Leo Versteegen","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-12-14T15:07:08Z","title":"A faster algorithm for Cops and Robbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07449","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":"sha256:21a8000c84226e1b6342e8436d9337146412e72a56cd306fd8f2ee57afebf99d","target":"record","created_at":"2026-07-05T04:31:58Z","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":"e1c8feb4e1c5cbc1025e5a2f6ed099a059df090dd28adef89f30bdefac3f1f83","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-12-14T15:07:08Z","title_canon_sha256":"313c949689b0286331ac911f725704b994eca46f23aca4e67d3d429e982d5355"},"schema_version":"1.0","source":{"id":"2112.07449","kind":"arxiv","version":2}},"canonical_sha256":"205520c94cb7d04092570b10964210edebe1dbb52ec958ff01fa4399a3ee70e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"205520c94cb7d04092570b10964210edebe1dbb52ec958ff01fa4399a3ee70e0","first_computed_at":"2026-07-05T04:31:58.373147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:31:58.373147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQnh96gmjZpUJlvVKpFsWuX5APjGxxl9QvNHZg8uWDN4tLzZAf88P9WsWwYiRbwuHFgrAUFjVmL/zJI/ZpQZBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:31:58.373706Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.07449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21a8000c84226e1b6342e8436d9337146412e72a56cd306fd8f2ee57afebf99d","sha256:377072c725657f79f5be88da06416834e24788f5ca222969ae6ca47f34ac5f30"],"state_sha256":"b44d1f16ce1543d5ceaa4e382307673595080b1a1bcc785bf2026384d02644f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3inRQtENRiw7NkCc9zzWf4MkORYamtsqMg/P85ZSrYLFva4wssM+cppH/gQNMLMOyCNIb5cfsgtZuVdX5NRWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T10:05:53.712620Z","bundle_sha256":"2dbcc6bcb4c51e59363c1e07435b50120e3057ddcb85e80d2b46147d8823f405"}}