{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:567Z43RGY5YGRQU3FNW5L5C35N","short_pith_number":"pith:567Z43RG","schema_version":"1.0","canonical_sha256":"efbf9e6e26c77068c29b2b6dd5f45beb66f2b8fe8c77d5de74968225a90988a0","source":{"kind":"arxiv","id":"1501.06596","version":1},"attestation_state":"computed","paper":{"title":"Sawtooth models and asymptotic independence in large compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Pierre Tarrago","submitted_at":"2015-01-26T21:46:50Z","abstract_excerpt":"In this paper we improve the probabilistic approach to compositions of Ehrenborg, Levin and Readdy by introducing a simpler but more general probabilistic model. As consequence we get some new estimates on the behavior of a uniform random permutation $\\sigma$ having a fixed descent set. In particular we show that independently of the shape of the descent set, $\\sigma(i)$ and $\\sigma(j)$ become independent when $i-j$ tends to $+\\infty$."},"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":"1501.06596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-26T21:46:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d01b501a0e09708c804660e4d1f29241fd2affe763726e6ba354390cb691608","abstract_canon_sha256":"a1d6ad3c75f571afde44fdf56b462e5799207c276fd6c247ec4e46c1a7e351f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:39.529900Z","signature_b64":"fxUvTYHNE7KjIZXjSw6B9Mo4q9+rdHwmWnd6iGC7QN/5nS+wmv3Scdt6EYLvaRmRClM1BWbK0z0JaXhCOr/vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efbf9e6e26c77068c29b2b6dd5f45beb66f2b8fe8c77d5de74968225a90988a0","last_reissued_at":"2026-05-18T02:28:39.529229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:39.529229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sawtooth models and asymptotic independence in large compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Pierre Tarrago","submitted_at":"2015-01-26T21:46:50Z","abstract_excerpt":"In this paper we improve the probabilistic approach to compositions of Ehrenborg, Levin and Readdy by introducing a simpler but more general probabilistic model. As consequence we get some new estimates on the behavior of a uniform random permutation $\\sigma$ having a fixed descent set. In particular we show that independently of the shape of the descent set, $\\sigma(i)$ and $\\sigma(j)$ become independent when $i-j$ tends to $+\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06596","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":"1501.06596","created_at":"2026-05-18T02:28:39.529333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06596v1","created_at":"2026-05-18T02:28:39.529333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06596","created_at":"2026-05-18T02:28:39.529333+00:00"},{"alias_kind":"pith_short_12","alias_value":"567Z43RGY5YG","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"567Z43RGY5YGRQU3","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"567Z43RG","created_at":"2026-05-18T12:29:05.191682+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/567Z43RGY5YGRQU3FNW5L5C35N","json":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N.json","graph_json":"https://pith.science/api/pith-number/567Z43RGY5YGRQU3FNW5L5C35N/graph.json","events_json":"https://pith.science/api/pith-number/567Z43RGY5YGRQU3FNW5L5C35N/events.json","paper":"https://pith.science/paper/567Z43RG"},"agent_actions":{"view_html":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N","download_json":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N.json","view_paper":"https://pith.science/paper/567Z43RG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06596&json=true","fetch_graph":"https://pith.science/api/pith-number/567Z43RGY5YGRQU3FNW5L5C35N/graph.json","fetch_events":"https://pith.science/api/pith-number/567Z43RGY5YGRQU3FNW5L5C35N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N/action/storage_attestation","attest_author":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N/action/author_attestation","sign_citation":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N/action/citation_signature","submit_replication":"https://pith.science/pith/567Z43RGY5YGRQU3FNW5L5C35N/action/replication_record"}},"created_at":"2026-05-18T02:28:39.529333+00:00","updated_at":"2026-05-18T02:28:39.529333+00:00"}