{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BYRW6K4ZZPVTY4CNVY2EPDELRY","short_pith_number":"pith:BYRW6K4Z","schema_version":"1.0","canonical_sha256":"0e236f2b99cbeb3c704dae34478c8b8e2ec3519505b160f587be33a2850decdb","source":{"kind":"arxiv","id":"1610.01479","version":1},"attestation_state":"computed","paper":{"title":"The recurrence function of a random Sturmian word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DM","authors_text":"Brigitte Vallee, Pablo Rotondo","submitted_at":"2016-10-05T15:21:20Z","abstract_excerpt":"This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian word. This parameter is central to combinatorics of words. Having fixed a possible length $n$ for the factors, we let $\\alpha$ to be drawn uniformly from the unit interval $[0,1]$, thus defining a random Sturmian word of slope $\\alpha$. Thus the waiting time for these factors becomes a random variable, for which we study the limit distribution and the limit de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.01479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-10-05T15:21:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c250805a7c234e1b96be5a427b971bcdcdb8eb16f2b01bd83acec75d3f40aa88","abstract_canon_sha256":"89526d56c0537c60fa6ff711883e505b4543e8f4d622d2c83e849fa4a6e01a17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:07.079885Z","signature_b64":"XXKi8k8N3tpa8CxDWhKbHDGI//P49d2bl/mlRKEk7XmSHFHPgVc1ivCzG4r75vy863cN/f3N8DUja9abMLbVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e236f2b99cbeb3c704dae34478c8b8e2ec3519505b160f587be33a2850decdb","last_reissued_at":"2026-05-18T01:03:07.079342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:07.079342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The recurrence function of a random Sturmian word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DM","authors_text":"Brigitte Vallee, Pablo Rotondo","submitted_at":"2016-10-05T15:21:20Z","abstract_excerpt":"This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian word. This parameter is central to combinatorics of words. Having fixed a possible length $n$ for the factors, we let $\\alpha$ to be drawn uniformly from the unit interval $[0,1]$, thus defining a random Sturmian word of slope $\\alpha$. Thus the waiting time for these factors becomes a random variable, for which we study the limit distribution and the limit de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01479","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.01479","created_at":"2026-05-18T01:03:07.079433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01479v1","created_at":"2026-05-18T01:03:07.079433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01479","created_at":"2026-05-18T01:03:07.079433+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYRW6K4ZZPVT","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYRW6K4ZZPVTY4CN","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYRW6K4Z","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY","json":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY.json","graph_json":"https://pith.science/api/pith-number/BYRW6K4ZZPVTY4CNVY2EPDELRY/graph.json","events_json":"https://pith.science/api/pith-number/BYRW6K4ZZPVTY4CNVY2EPDELRY/events.json","paper":"https://pith.science/paper/BYRW6K4Z"},"agent_actions":{"view_html":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY","download_json":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY.json","view_paper":"https://pith.science/paper/BYRW6K4Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01479&json=true","fetch_graph":"https://pith.science/api/pith-number/BYRW6K4ZZPVTY4CNVY2EPDELRY/graph.json","fetch_events":"https://pith.science/api/pith-number/BYRW6K4ZZPVTY4CNVY2EPDELRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY/action/storage_attestation","attest_author":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY/action/author_attestation","sign_citation":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY/action/citation_signature","submit_replication":"https://pith.science/pith/BYRW6K4ZZPVTY4CNVY2EPDELRY/action/replication_record"}},"created_at":"2026-05-18T01:03:07.079433+00:00","updated_at":"2026-05-18T01:03:07.079433+00:00"}