{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KDDESUWSSOE6BB5CW6AV62DBYT","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":"e3447ca4493de0ec43ca39a206d880218a0b7489a972ff06049a79f4e6f0dd8f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-10-26T12:59:22Z","title_canon_sha256":"ac6a94a31ebd2c839138b05136b17b5854d19590fafe9f80840a9bc412af6f9d"},"schema_version":"1.0","source":{"id":"1510.07462","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07462","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07462v2","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07462","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"pith_short_12","alias_value":"KDDESUWSSOE6","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KDDESUWSSOE6BB5C","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KDDESUWS","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:6b6add92f2d401f80445284089c1a3d4652b004e4d8a7bc751fdc099984fe0cf","target":"graph","created_at":"2026-05-18T00:53:21Z","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":"Disjoint-Set forests, consisting of Union-Find trees are data structures having a widespread practical application due to their efficiency. Despite them being well-known, no exact structural characterization of these trees is known (such a characterization exists for Union trees which are constructed without using path compression). In this paper we provide such a characterization and show that the decision problem whether a given tree is a Union-Find tree is $\\NP$-complete.","authors_text":"Kitti Gelle, Szabolcs Ivan","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-10-26T12:59:22Z","title":"Recognizing Union-Find trees is NP-complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07462","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":"sha256:5c19643c0a23bd8ace735d536bd32933c8877fba2922a47e4865d6f6594856e6","target":"record","created_at":"2026-05-18T00:53:21Z","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":"e3447ca4493de0ec43ca39a206d880218a0b7489a972ff06049a79f4e6f0dd8f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-10-26T12:59:22Z","title_canon_sha256":"ac6a94a31ebd2c839138b05136b17b5854d19590fafe9f80840a9bc412af6f9d"},"schema_version":"1.0","source":{"id":"1510.07462","kind":"arxiv","version":2}},"canonical_sha256":"50c64952d29389e087a2b7815f6861c4c2d2f50e80f62fb385d97f3624c491b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50c64952d29389e087a2b7815f6861c4c2d2f50e80f62fb385d97f3624c491b9","first_computed_at":"2026-05-18T00:53:21.080207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:21.080207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YGDUo0FLdXvKn8UcK+SXwVw/Fr3Ko02i8y0aS554GHux92CkIxzYF9dmYHkTRJZzw1+nIUgoR+IEIhmQ7qGqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:21.080659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07462","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c19643c0a23bd8ace735d536bd32933c8877fba2922a47e4865d6f6594856e6","sha256:6b6add92f2d401f80445284089c1a3d4652b004e4d8a7bc751fdc099984fe0cf"],"state_sha256":"dc6248e176bf5a419d90993e1fa11317448c095887d9938638ba3b37208ce34b"}