{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BLFJXXKVUWKJXBWWKWN2BY3AX4","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":"979d76fdaad1d1e87e6e84114ccff489a37331107b91349d4b5eed28f4037c28","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-23T13:24:16Z","title_canon_sha256":"620ad3339dd5f24d9502f47ef3e5fb818f6ac6a2e0efb5cceb4cef1c4a5b851b"},"schema_version":"1.0","source":{"id":"1406.5895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5895","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5895v1","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5895","created_at":"2026-05-18T02:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"BLFJXXKVUWKJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BLFJXXKVUWKJXBWW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BLFJXXKV","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:28f595442d41c849f650ee5f9ddbf6dbec8cf52b6c2fb592cf846ece061670e4","target":"graph","created_at":"2026-05-18T02:47:43Z","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 word $w$ over an alphabet $\\Sigma$ is a Lyndon word if there exists an order defined on $\\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \\emph{universal Lyndon words}, which are words over an $n$-letter alphabet that have length $n!$ and such that all the conjugates are Lyndon words. We show that universal Lyndon words exist for every $n$ and exhibit combinatorial and structural properties of these words. We then define particular prefix codes, which we call Hamiltonian lex-codes, and show that every Hamiltonian lex-co","authors_text":"Arturo Carpi, Gabriele Fici, Jakub Oprsal, Marinella Sciortino, Stepan Holub","cross_cats":["cs.FL","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-23T13:24:16Z","title":"Universal Lyndon Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5895","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":"sha256:53007c0fee7b568c6f9e073141d8752a0b354e7ebd7d6ab8c07050a388b15d62","target":"record","created_at":"2026-05-18T02:47:43Z","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":"979d76fdaad1d1e87e6e84114ccff489a37331107b91349d4b5eed28f4037c28","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-23T13:24:16Z","title_canon_sha256":"620ad3339dd5f24d9502f47ef3e5fb818f6ac6a2e0efb5cceb4cef1c4a5b851b"},"schema_version":"1.0","source":{"id":"1406.5895","kind":"arxiv","version":1}},"canonical_sha256":"0aca9bdd55a5949b86d6559ba0e360bf3619c9a0926b49488d6b9cbba7b15efa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aca9bdd55a5949b86d6559ba0e360bf3619c9a0926b49488d6b9cbba7b15efa","first_computed_at":"2026-05-18T02:47:43.639722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:43.639722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OByRLO/kUTL4icNLyRIA55AMgBWfRRSMdiedWazCLPHRAbyctjmR7exhGJlTFBchAYzR5X3u41q52IdZnLu/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:43.640543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53007c0fee7b568c6f9e073141d8752a0b354e7ebd7d6ab8c07050a388b15d62","sha256:28f595442d41c849f650ee5f9ddbf6dbec8cf52b6c2fb592cf846ece061670e4"],"state_sha256":"749305378cb6a12aec8ba54224251a8a0b0258bda47064999faa749909c13ff3"}