{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JMYIGYPJ646RJOQK2WLPPIRY4Q","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":"1ed1a2416cd7ee68efdb65ab8238c8c473fde63a048054f1f62a435656ea2fc6","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T12:12:54Z","title_canon_sha256":"4db06bb5019977b3a12e55234434cc88ec48f03ebb7bf9248a726a9f613b200a"},"schema_version":"1.0","source":{"id":"1906.11012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11012","created_at":"2026-05-17T23:42:10Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11012v1","created_at":"2026-05-17T23:42:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11012","created_at":"2026-05-17T23:42:10Z"},{"alias_kind":"pith_short_12","alias_value":"JMYIGYPJ646R","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JMYIGYPJ646RJOQK","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JMYIGYPJ","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:7524e1c70c79e31832823e3a0d726a193022fe1fc2fa143cf57fa0b6866eb3c9","target":"graph","created_at":"2026-05-17T23:42:10Z","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":"In the coupon collector problem with $n$ items, the collector needs a random number of tries $T_n\\simeq n\\ln n$ to complete the collection. Also, after $nt$ tries, the collector has secured approximately a fraction $\\zeta_\\infty(t)=1-e^{-t}$ of the complete collection, so we call $\\zeta_\\infty$ the (asymptotic) \\emph{completion curve}.  In this paper, for $\\nu>0$, we address the asymptotic shape $\\zeta (\\nu,.) $ of the completion curve under the condition $T_n\\leq \\left( 1+\\nu \\right) n$, i.e. assuming that the collection is \\emph{completed unlikely fast}. As an application to the asymptotic s","authors_text":"Anis Amri (IECL), Philippe Chassaing (IECL)","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T12:12:54Z","title":"The impatient collector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11012","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":"sha256:00f005453bac6a165744d82b6990e499bbea20ece86a15cf2bcb0eeeb56c9f18","target":"record","created_at":"2026-05-17T23:42:10Z","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":"1ed1a2416cd7ee68efdb65ab8238c8c473fde63a048054f1f62a435656ea2fc6","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T12:12:54Z","title_canon_sha256":"4db06bb5019977b3a12e55234434cc88ec48f03ebb7bf9248a726a9f613b200a"},"schema_version":"1.0","source":{"id":"1906.11012","kind":"arxiv","version":1}},"canonical_sha256":"4b308361e9f73d14ba0ad596f7a238e40ce456f702055512af52d86ca31f88e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b308361e9f73d14ba0ad596f7a238e40ce456f702055512af52d86ca31f88e6","first_computed_at":"2026-05-17T23:42:10.264994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:10.264994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e1wCGnS2/GvwoWkfUmzxwU/eQFV9f/cFbVwPbtUU+KJAXuXg1NQjy4Yvyu3+PjO4XEl9biyL1YeCKXGfGMbwAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:10.265810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f005453bac6a165744d82b6990e499bbea20ece86a15cf2bcb0eeeb56c9f18","sha256:7524e1c70c79e31832823e3a0d726a193022fe1fc2fa143cf57fa0b6866eb3c9"],"state_sha256":"d6ee8f96953177103b8369f14d790366e09144458a9836dc367ffe3a29345525"}