{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O422KA6VBFPXL3A7Q274Q5NFPQ","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":"fb367af45b25c4dbe8c1e5f8e213da3ebb920b2a83e5eb7c405dd9d1b81ec179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-23T23:17:50Z","title_canon_sha256":"641b6fef9588d38cf92adbfe7ec6e33d799bddbd0ad25f084109b2ee3df05f7a"},"schema_version":"1.0","source":{"id":"1803.09009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09009","created_at":"2026-05-18T00:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09009v2","created_at":"2026-05-18T00:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09009","created_at":"2026-05-18T00:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"O422KA6VBFPX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O422KA6VBFPXL3A7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O422KA6V","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:d5b2ffe0d30d6614e9d246ba19fefd3aaff35e9f4c91027ebb92d4b6667f6c2f","target":"graph","created_at":"2026-05-18T00:12:38Z","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 present sufficient conditions for when an ordering of universal cycles $\\alpha_1, \\alpha_2, \\ldots, \\alpha_m$ for disjoint sets $\\mathbf{S}_1, \\mathbf{S}_2, \\ldots , \\mathbf{S}_m$ can be concatenated together to obtain a universal cycle for $\\mathbf{S} = \\mathbf{S}_1 \\cup \\mathbf{S}_2 \\cup \\cdots \\cup \\mathbf{S}_m$. When $\\mathbf{S}$ is the set of all $k$-ary strings of length $n$, the result of such a successful construction is a de Bruijn sequence. Our conditions are applied to generalize two previously known de Bruijn sequence constructions and then they are applied to develop three new ","authors_text":"Daniel Gabric, Joe Sawada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-23T23:17:50Z","title":"Constructing de Bruijn sequences by concatenating smaller universal cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09009","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":"sha256:19878b712a756972f40a4be131fb9680c90c966a84da715c8fa624385b4fdb8b","target":"record","created_at":"2026-05-18T00:12:38Z","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":"fb367af45b25c4dbe8c1e5f8e213da3ebb920b2a83e5eb7c405dd9d1b81ec179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-23T23:17:50Z","title_canon_sha256":"641b6fef9588d38cf92adbfe7ec6e33d799bddbd0ad25f084109b2ee3df05f7a"},"schema_version":"1.0","source":{"id":"1803.09009","kind":"arxiv","version":2}},"canonical_sha256":"7735a503d5095f75ec1f86bfc875a57c2584d210ef6c99ebef0f5cd0c3f525a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7735a503d5095f75ec1f86bfc875a57c2584d210ef6c99ebef0f5cd0c3f525a9","first_computed_at":"2026-05-18T00:12:38.081255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:38.081255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fa2f6nU5D3Bm+XlW4HQ2OVUqrt59IkjdeIJuGuEFJANxMfvOQEhGsxc0YwtlSufvtB2MrstOf5bOL78HcVUCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:38.081911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19878b712a756972f40a4be131fb9680c90c966a84da715c8fa624385b4fdb8b","sha256:d5b2ffe0d30d6614e9d246ba19fefd3aaff35e9f4c91027ebb92d4b6667f6c2f"],"state_sha256":"b355c49df9c121f4e4c28c770bc8e1a05a5bfa084a132aae8c07dfbb23b69d74"}