{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WU6ANEWYE5VIOGTCO2J3AIVDRG","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":"667faef27554e92c9fe7acc8fbc7f5af1e7e9bf1823918eb51e43cd82c07315d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-19T14:01:40Z","title_canon_sha256":"68c8379ddca476361e52e96f040bc6b0096a55e71a1308bea8948d3d1a859a31"},"schema_version":"1.0","source":{"id":"2605.19870","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19870","created_at":"2026-05-20T01:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19870v1","created_at":"2026-05-20T01:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19870","created_at":"2026-05-20T01:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"WU6ANEWYE5VI","created_at":"2026-05-20T01:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"WU6ANEWYE5VIOGTC","created_at":"2026-05-20T01:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"WU6ANEWY","created_at":"2026-05-20T01:06:18Z"}],"graph_snapshots":[{"event_id":"sha256:2135aec7592e99e8b34e1f301819608eb583517f8ede5ff51dee8daf26ae532e","target":"graph","created_at":"2026-05-20T01:06:18Z","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/2605.19870/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The \\textsc{Co-Path Packing} (resp., \\textsc{Co-Path Set}) problem asks whether a given graph can be edited to a collection of induced paths by deleting at most $k$ vertices (resp., $k$ edges). Both are fundamental problems with significant applications in bioinformatics and have been extensively studied within the framework of exact and parameterized algorithms. Currently, the state-of-the-art approach utilizes the randomized ``Cut \\& Count'' technique, which solves \\textsc{Co-Path Set} in $O^*(4^{\\mathbf{tw}})$ time and \\textsc{Co-Path Packing} in $O^*(5^{\\mathbf{pw}})$ time, where $\\mathbf{","authors_text":"Kangyi Tian, Mingyu Xiao, Yuxi Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-19T14:01:40Z","title":"Deterministic Single Exponential Time Algorithms for Co-Path Packing and Co-Path Set Parameterized by Treewidth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19870","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:c79c9951618edf14a76226baf95933343fcbeb287cdad77396d1150d640315ed","target":"record","created_at":"2026-05-20T01:06:18Z","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":"667faef27554e92c9fe7acc8fbc7f5af1e7e9bf1823918eb51e43cd82c07315d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-19T14:01:40Z","title_canon_sha256":"68c8379ddca476361e52e96f040bc6b0096a55e71a1308bea8948d3d1a859a31"},"schema_version":"1.0","source":{"id":"2605.19870","kind":"arxiv","version":1}},"canonical_sha256":"b53c0692d8276a871a627693b022a389aff3b8622b4cff7aa1035e7517cc7568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b53c0692d8276a871a627693b022a389aff3b8622b4cff7aa1035e7517cc7568","first_computed_at":"2026-05-20T01:06:18.396718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:06:18.396718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y7ofotXdM4iYxW4+AU7lx8rbZugYV9SrQZ+dIkup5RFYQDpDWknPpDepvrAV2et5hhO88UgyzosZijpKf+eTCg==","signature_status":"signed_v1","signed_at":"2026-05-20T01:06:18.397352Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19870","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c79c9951618edf14a76226baf95933343fcbeb287cdad77396d1150d640315ed","sha256:2135aec7592e99e8b34e1f301819608eb583517f8ede5ff51dee8daf26ae532e"],"state_sha256":"b4422414edccabf91226f34bb74481933fc7e4b4437ccf8dd09d5857eb3340f0"}