{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2PTRYKKYBBVD2OONQTPHSVWC7V","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":"10c61004f5ff1c56d79380f54fee6d3a772a275463d34384366e2b5b1d3da8a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:01:50Z","title_canon_sha256":"b4f4da8bfd7384e194e934a3913fe7a3966c6ef26744bc567df12b9c5a6b7eb4"},"schema_version":"1.0","source":{"id":"1510.08276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08276","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08276v1","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08276","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"pith_short_12","alias_value":"2PTRYKKYBBVD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2PTRYKKYBBVD2OON","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2PTRYKKY","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:e9003c50e7628008b52c6dac52eb2d3beada8f268391f7965be52aa4794cf85d","target":"graph","created_at":"2026-05-18T01:28:36Z","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":"A vertex set $X$ of a graph $G$ is an association set if each component of $G - X$ is a clique, or a dissociation set if each component of $G - X$ is a single vertex or a single edge. Interestingly, $G - X$ is then precisely a graph containing no induced $P_3$'s or containing no $P_3$'s, respectively. We observe some special structures and show that if none of them exists, then the minimum association set problem can be reduced to the minimum (weighted) dissociation set problem. This yields the first nontrivial approximation algorithm for association set, and its approximation ratio is 2.5, ma","authors_text":"Jianxin Wang, Jie You, Yixin Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:01:50Z","title":"Approximate Association via Dissociation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08276","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":"sha256:8dc6ff74f1d18c8761b52834d094a995aaeaaf9c603d13ef01204179eaa49fa0","target":"record","created_at":"2026-05-18T01:28:36Z","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":"10c61004f5ff1c56d79380f54fee6d3a772a275463d34384366e2b5b1d3da8a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:01:50Z","title_canon_sha256":"b4f4da8bfd7384e194e934a3913fe7a3966c6ef26744bc567df12b9c5a6b7eb4"},"schema_version":"1.0","source":{"id":"1510.08276","kind":"arxiv","version":1}},"canonical_sha256":"d3e71c2958086a3d39cd84de7956c2fd4c7b77b37ca3e728f4b02f55acfbbc13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3e71c2958086a3d39cd84de7956c2fd4c7b77b37ca3e728f4b02f55acfbbc13","first_computed_at":"2026-05-18T01:28:36.614079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:36.614079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuRsWZpXy2xxgaYp3qRgpHnZ7toYc9PPB6P2yBBsJ0SYnR7IuKDQCexOHLkyhIsEA7lNF6JqL91mGfz8mHvRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:36.614737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dc6ff74f1d18c8761b52834d094a995aaeaaf9c603d13ef01204179eaa49fa0","sha256:e9003c50e7628008b52c6dac52eb2d3beada8f268391f7965be52aa4794cf85d"],"state_sha256":"4f359c02ebcccc70bf788a254699bba44cef5fc9e9d458e650f92738b150f33d"}