{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JZME2AWHSANCRQ2WVRB2LEVYAH","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":"b16c3d4375c061d5d1f3e3861aef2e8f97529b1a4b8e0d5fc5afba6a57140c19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T15:19:33Z","title_canon_sha256":"3ad6dc5609c54d84e4fafdcaecea66354576f843a68ccae1b4fc271060196156"},"schema_version":"1.0","source":{"id":"1604.05999","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05999","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05999v1","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05999","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"JZME2AWHSANC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JZME2AWHSANCRQ2W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JZME2AWH","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:edbd0e5390e2f427e50240b1124623f6dea8cd3367cf0ff323ed3ff31a35348a","target":"graph","created_at":"2026-05-18T01:16:33Z","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":"We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth $\\mathcal{O}(\\sqrt{k}\\log k)$, and (ii) for every connected subgraph $H$ of $G$ on at most $k$ vertices, the probability that $A$ covers the whole vertex set of $H$ is at least $(2^{\\mathcal{O}(\\sqrt{k}\\log^2 k)}\\cdot n^{\\mathcal{O}(1)})^{-1}$, where $n$ is the number of vertices of $G$.\n  Together with standard dynamic programming techniques for graphs of b","authors_text":"Daniel Lokshtanov, D\\'aniel Marx, Fedor V. Fomin, Marcin Pilipczuk, Micha{\\l} Pilipczuk, Saket Saurabh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T15:19:33Z","title":"Subexponential parameterized algorithms for planar and apex-minor-free graphs via low treewidth pattern covering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05999","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:b2f8b5e015a51eb2984ade3f2dbde38efab5c596d05b7d612dd0a29f552ef2ae","target":"record","created_at":"2026-05-18T01:16:33Z","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":"b16c3d4375c061d5d1f3e3861aef2e8f97529b1a4b8e0d5fc5afba6a57140c19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T15:19:33Z","title_canon_sha256":"3ad6dc5609c54d84e4fafdcaecea66354576f843a68ccae1b4fc271060196156"},"schema_version":"1.0","source":{"id":"1604.05999","kind":"arxiv","version":1}},"canonical_sha256":"4e584d02c7901a28c356ac43a592b801e3b99d036128342087b9b31c0e4844ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e584d02c7901a28c356ac43a592b801e3b99d036128342087b9b31c0e4844ae","first_computed_at":"2026-05-18T01:16:33.973561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.973561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KB89hcXujQsvOQclAyJtCwPih206ooISYls6F5A+ezR+z/Gb+fFM74ZraI6Z/gNV+Ybhb1NQwo8Js2AgsjqOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.974227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05999","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2f8b5e015a51eb2984ade3f2dbde38efab5c596d05b7d612dd0a29f552ef2ae","sha256:edbd0e5390e2f427e50240b1124623f6dea8cd3367cf0ff323ed3ff31a35348a"],"state_sha256":"995827bb21fb520bfbb075e87705ac705395b8852a2eb21feca15af0fc70122d"}