{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IODET7F5B5B2F5LECWEFXJK4HH","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":"1e2fa75bfbf5b5c42274c779daebdf9e1af843ca5063243dc9bea678caec9f24","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-14T12:20:20Z","title_canon_sha256":"30bb7c629d22abb0a7571ff9d11d03fa520318e62f0a580b3e0862ba255f3275"},"schema_version":"1.0","source":{"id":"1412.4346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4346","created_at":"2026-05-18T02:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4346v1","created_at":"2026-05-18T02:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4346","created_at":"2026-05-18T02:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"IODET7F5B5B2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IODET7F5B5B2F5LE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IODET7F5","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:ee7c8e777289ffb12cfc860fd323db10412dde2f2b8e256cdb294b084d9d9083","target":"graph","created_at":"2026-05-18T02:31:19Z","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":"The following variant of the collector's problem has attracted considerable attention relatively recently (see, e.g., N. Pintacuda 1980, D. Foata H. Guo-Niu and B. Lass 2001, D. Foata and D. Zeilberger 2003, I. Adler, S. Oren and S. Ross 2003, and S. Ross 2010): There is one main collector who collects coupons. Assume there are $N$ different types of coupons with, in general, unequal occurring probabilities. When the main collector gets a \"double\", she gives it to her older brother; when this brother gets a \"double\", he gives it to the next brother, and so on. Hence, when the main collector co","authors_text":"Aristides V. Doumas, Vassilis G. Papanicolaou","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-14T12:20:20Z","title":"The Siblings of the Coupon Collector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4346","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:b45f652d61a6e79116135fc063b7fbb5e1294d3f245a2617124d2a2f41be17ea","target":"record","created_at":"2026-05-18T02:31:19Z","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":"1e2fa75bfbf5b5c42274c779daebdf9e1af843ca5063243dc9bea678caec9f24","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-14T12:20:20Z","title_canon_sha256":"30bb7c629d22abb0a7571ff9d11d03fa520318e62f0a580b3e0862ba255f3275"},"schema_version":"1.0","source":{"id":"1412.4346","kind":"arxiv","version":1}},"canonical_sha256":"438649fcbd0f43a2f56415885ba55c39f958e0ab321ebdde6f1211e627f7e0f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"438649fcbd0f43a2f56415885ba55c39f958e0ab321ebdde6f1211e627f7e0f9","first_computed_at":"2026-05-18T02:31:19.493310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:19.493310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"So7Dr45H5sKSASXTLQtkvXW4O/44TW2xs7MaowwAo5hwJi9xJPd7KpT9UrO2V9jW83eL0KurO5oOs05jP0HoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:19.493977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b45f652d61a6e79116135fc063b7fbb5e1294d3f245a2617124d2a2f41be17ea","sha256:ee7c8e777289ffb12cfc860fd323db10412dde2f2b8e256cdb294b084d9d9083"],"state_sha256":"a8772efa3be5e165575f5f3803dc674cc5a42757a2479d68fc30f3ef91d7cc6b"}