{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DCSKF4C5GM4PZ2UN6O5GL6XNH5","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":"18a58754ba9bcfefde0b1cad2e97c53712d262a6d99d0d0c4afaed8adfa28f30","cross_cats_sorted":["cs.DM","math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-10T12:18:44Z","title_canon_sha256":"138120dd34ab537e287d1ae3df1a25aa875d4d9defa840f035a51a74d07c5a3a"},"schema_version":"1.0","source":{"id":"1503.02880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02880","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02880v1","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02880","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"DCSKF4C5GM4P","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DCSKF4C5GM4PZ2UN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DCSKF4C5","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:7c8e8662397f03ae9570edd50d487932247e95f6315fbbc554b4b4990106ce96","target":"graph","created_at":"2026-05-18T02:25:12Z","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 give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form $n^{\\epsilon}$ in the case when the power law exponent satisfies $\\beta <1$. In the case when $\\beta =1$, the lower bound is of the form $\\log (n)^{\\epsilon}$. The embedding technique used in the proof could also be of independent interest.","authors_text":"Marek Karpinski, Mathias Hauptmann","cross_cats":["cs.DM","math.CO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-10T12:18:44Z","title":"On the Approximability of Independent Set Problem on Power Law Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02880","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":"sha256:706f5c400d6c51a99e10db90fb34f1255c930f49a4e8851f31d85d58491cd21c","target":"record","created_at":"2026-05-18T02:25:12Z","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":"18a58754ba9bcfefde0b1cad2e97c53712d262a6d99d0d0c4afaed8adfa28f30","cross_cats_sorted":["cs.DM","math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-10T12:18:44Z","title_canon_sha256":"138120dd34ab537e287d1ae3df1a25aa875d4d9defa840f035a51a74d07c5a3a"},"schema_version":"1.0","source":{"id":"1503.02880","kind":"arxiv","version":1}},"canonical_sha256":"18a4a2f05d3338fcea8df3ba65faed3f4867ffe7707e92c61264a4dd63548e2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18a4a2f05d3338fcea8df3ba65faed3f4867ffe7707e92c61264a4dd63548e2b","first_computed_at":"2026-05-18T02:25:12.849134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:12.849134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yu6L6U18jJ5wpfpZ2P/Pu1Awm4gtZa6n1WpLmxgwVNetfac33FI/jVZfsm5lu+ToaDRO/hQrWuoH0c1ZDS9cCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:12.849714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:706f5c400d6c51a99e10db90fb34f1255c930f49a4e8851f31d85d58491cd21c","sha256:7c8e8662397f03ae9570edd50d487932247e95f6315fbbc554b4b4990106ce96"],"state_sha256":"18fd5a1afe5a2014da66b10b9edbf1b93a2bbeaebe79bb6c44ec4de4396b72fd"}