{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IZH5UOUHKRAM6F42AD5POEN436","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":"50fe11c94fdae9f403ae3bf3b9ff12ce58c36b3f0bfb9523c0148bd6e7092a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-19T14:20:37Z","title_canon_sha256":"94561bb2e50a58c8e8735d69c92e30e3f800fba7716cd1013a1d50b3cd883c46"},"schema_version":"1.0","source":{"id":"1707.06110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06110","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06110v2","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06110","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"IZH5UOUHKRAM","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IZH5UOUHKRAM6F42","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IZH5UOUH","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:6bedcc3826d0c2c31d00ff18c7d7471092f6d7bb05b63eb27572212d558ff07a","target":"graph","created_at":"2026-05-18T00:01:53Z","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":"This paper initiates the study of shortening universal cycles (u-cycles) and universal words (u-words) for permutations either by using incomparable elements, or by using non-deterministic symbols. The latter approach is similar in nature to the recent relevant studies for the de Bruijn sequences. A particular result we obtain in this paper is that u-words for $n$-permutations exist of lengths $n!+(1-k)(n-1)$ for $k=0,1,\\ldots,(n-2)!$.","authors_text":"Sergey Kitaev, Vincent Vajnovszki, Vladimir N. Potapov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-19T14:20:37Z","title":"On shortening u-cycles and u-words for permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06110","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:b0def278fae86c62fd16c11e2f9b8e61e9571df75b769660757eb371e5f45ad9","target":"record","created_at":"2026-05-18T00:01:53Z","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":"50fe11c94fdae9f403ae3bf3b9ff12ce58c36b3f0bfb9523c0148bd6e7092a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-19T14:20:37Z","title_canon_sha256":"94561bb2e50a58c8e8735d69c92e30e3f800fba7716cd1013a1d50b3cd883c46"},"schema_version":"1.0","source":{"id":"1707.06110","kind":"arxiv","version":2}},"canonical_sha256":"464fda3a875440cf179a00faf711bcdfad6cc8938c6c8424b1d16ad5b464c523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"464fda3a875440cf179a00faf711bcdfad6cc8938c6c8424b1d16ad5b464c523","first_computed_at":"2026-05-18T00:01:53.613830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:53.613830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"krpqDgu2BeeaopooXIQ3Ms6PAxFMv+fSbZ+2P5fv74Exn4s2Xy4TqW8QxxVfa5hb5wOH9Xa/HuoXhO4TSkkyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:53.614223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0def278fae86c62fd16c11e2f9b8e61e9571df75b769660757eb371e5f45ad9","sha256:6bedcc3826d0c2c31d00ff18c7d7471092f6d7bb05b63eb27572212d558ff07a"],"state_sha256":"d66f68ce461c28b6f30cfd09b64849b772f768e3dc0cf43b93a953f0d9236cf5"}