{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WLMEZLZ2IK5BXWGPXJYWS67D64","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":"e2fd1842f93bc24f6b939c258c60130ef58211ca4738d1151b1c6bc21affd0df","cross_cats_sorted":["cs.DM","cs.DS","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-01T10:24:05Z","title_canon_sha256":"ed526affbc6daa3752f5dd9e75ae6d59204d57b3f3b6b51c240b57518f27e740"},"schema_version":"1.0","source":{"id":"2302.00352","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.00352","created_at":"2026-07-05T07:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"2302.00352v3","created_at":"2026-07-05T07:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00352","created_at":"2026-07-05T07:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"WLMEZLZ2IK5B","created_at":"2026-07-05T07:59:34Z"},{"alias_kind":"pith_short_16","alias_value":"WLMEZLZ2IK5BXWGP","created_at":"2026-07-05T07:59:34Z"},{"alias_kind":"pith_short_8","alias_value":"WLMEZLZ2","created_at":"2026-07-05T07:59:34Z"}],"graph_snapshots":[{"event_id":"sha256:02e4e633f4ae6563766d80a879fadd650552fc4ae79bf47f312afd926005474c","target":"graph","created_at":"2026-07-05T07:59:34Z","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/2302.00352/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define new graph parameters, called flip-width, that generalize treewidth, degeneracy, and generalized coloring numbers for sparse graphs, and clique-width and twin-width for dense graphs. The flip-width parameters are defined using variants of the Cops and Robber game, in which the robber has speed bounded by a fixed constant $r\\in\\mathbb N\\cup\\{\\infty\\}$, and the cops perform flips (or perturbations) of the considered graph. We then propose a new notion of tameness of a graph class, called bounded flip-width, which is a dense counterpart of classes of bounded expansion of Ne\\v{s}etril and","authors_text":"Szymon Toru\\'nczyk","cross_cats":["cs.DM","cs.DS","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-01T10:24:05Z","title":"Flip-width: Cops and Robber on dense graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00352","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":"sha256:80970a6210278cfeb9ac796012022ed05977c8e5704510eae051aa832fa79847","target":"record","created_at":"2026-07-05T07:59:34Z","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":"e2fd1842f93bc24f6b939c258c60130ef58211ca4738d1151b1c6bc21affd0df","cross_cats_sorted":["cs.DM","cs.DS","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-01T10:24:05Z","title_canon_sha256":"ed526affbc6daa3752f5dd9e75ae6d59204d57b3f3b6b51c240b57518f27e740"},"schema_version":"1.0","source":{"id":"2302.00352","kind":"arxiv","version":3}},"canonical_sha256":"b2d84caf3a42ba1bd8cfba71697be3f72e982f08acf53cdc8cf9b9e6413d23c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2d84caf3a42ba1bd8cfba71697be3f72e982f08acf53cdc8cf9b9e6413d23c2","first_computed_at":"2026-07-05T07:59:34.358166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:59:34.358166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UohdUpy307Ep4K2a0pnzIQ0ZJPqF7S4bWtA2zOYFj4wb+GNwN/I6bhMnKVOuZoLL6SbmneGORpKcLpkQB5lpDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:59:34.358662Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.00352","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80970a6210278cfeb9ac796012022ed05977c8e5704510eae051aa832fa79847","sha256:02e4e633f4ae6563766d80a879fadd650552fc4ae79bf47f312afd926005474c"],"state_sha256":"087b422df15477c81a22ef5a866aa7340c6b6db9a7686ad4167f79da52e0d006"}