{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CGGMDHNZ2ATKFERJWZQ4PYHWHT","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":"50cbfbe83e59e48fe8e416bb8ba0b0d15f66c0b3ab3e7c6814b96b4386b96d35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:12:58Z","title_canon_sha256":"06fbf28eeb5939beb9efc945571a8b4cc9e87e59d81b6786aa4bc7a55ad32a49"},"schema_version":"1.0","source":{"id":"1507.02163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02163","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02163v2","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02163","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"CGGMDHNZ2ATK","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CGGMDHNZ2ATKFERJ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CGGMDHNZ","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:43bfd5cacda45319f5c3182ede94de3128194f57e907b914a5d5bdf6496f4686","target":"graph","created_at":"2026-05-18T01:34:15Z","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":"In the Independent set problem, the input is a graph $G$, every vertex has a non-negative integer weight, and the task is to find a set $S$ of pairwise non-adjacent vertices, maximizing the total weight of the vertices in $S$. We give an $n^{O (\\log^2 n)}$ time algorithm for this problem on graphs excluding the path $P_6$ on $6$ vertices as an induced subgraph. Currently, there is no constant $k$ known for which Independent Set on $P_{k}$-free graphs becomes NP-complete, and our result implies that if such a $k$ exists, then $k > 6$ unless all problems in NP can be decided in (quasi)polynomial","authors_text":"Daniel Lokshtanov, Erik Jan van Leeuwen, Marcin Pilipczuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:12:58Z","title":"Independence and Efficient Domination on $P_6$-free Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02163","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:fe860573c6ce40b78c21451d108167704ac71772c47412a7a11ded5ddd2dfd0a","target":"record","created_at":"2026-05-18T01:34:15Z","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":"50cbfbe83e59e48fe8e416bb8ba0b0d15f66c0b3ab3e7c6814b96b4386b96d35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:12:58Z","title_canon_sha256":"06fbf28eeb5939beb9efc945571a8b4cc9e87e59d81b6786aa4bc7a55ad32a49"},"schema_version":"1.0","source":{"id":"1507.02163","kind":"arxiv","version":2}},"canonical_sha256":"118cc19db9d026a29229b661c7e0f63ce7357d3e6f7b9a0d7272672f396dadb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"118cc19db9d026a29229b661c7e0f63ce7357d3e6f7b9a0d7272672f396dadb9","first_computed_at":"2026-05-18T01:34:15.684198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:15.684198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y2eLL3Xgu3hJnN2e54AcZkKGYHk6IChdwhnc4LqKHcxA95SZNTdIf7tRVOj0TERynm6Ch7KaMynwRStnihfvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:15.685007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe860573c6ce40b78c21451d108167704ac71772c47412a7a11ded5ddd2dfd0a","sha256:43bfd5cacda45319f5c3182ede94de3128194f57e907b914a5d5bdf6496f4686"],"state_sha256":"580da612ce527854d811329f91376ec511e836b0f4e1985879a03d0d3ac93a33"}