{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ULCCDFWWKKSG4S5R5BO4J7NAC6","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":"a6e348fcc97d521c41d1d8e8b921c14d718df064d89addf78684d61af777ad9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-16T12:39:23Z","title_canon_sha256":"dffccf3cc1a70d9748d3bcf552fa352c4cc074c2ef811d28ec20fbcb486a32bc"},"schema_version":"1.0","source":{"id":"1706.05250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05250","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05250v1","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05250","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"ULCCDFWWKKSG","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULCCDFWWKKSG4S5R","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULCCDFWW","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:a5f2fc2cec6aae0dccca56f61f18b7b98ca594b24b2007e831d0d3b111c6730a","target":"graph","created_at":"2026-05-18T00:42:14Z","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":"Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the expectation of the waiting time for a partial collection in the CCP, and the Miss rate of a LRU cache.","authors_text":"Christian Berthet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-16T12:39:23Z","title":"Contributions to the Generalized Coupon Collector and LRU Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05250","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:addacb381b198e918255313cb1e703883f2fe5d0933e7ac8d06a4337621a4e8e","target":"record","created_at":"2026-05-18T00:42:14Z","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":"a6e348fcc97d521c41d1d8e8b921c14d718df064d89addf78684d61af777ad9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-16T12:39:23Z","title_canon_sha256":"dffccf3cc1a70d9748d3bcf552fa352c4cc074c2ef811d28ec20fbcb486a32bc"},"schema_version":"1.0","source":{"id":"1706.05250","kind":"arxiv","version":1}},"canonical_sha256":"a2c42196d652a46e4bb1e85dc4fda017ae77b0e112a98da93f79063c0be25a91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c42196d652a46e4bb1e85dc4fda017ae77b0e112a98da93f79063c0be25a91","first_computed_at":"2026-05-18T00:42:14.323998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:14.323998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FluISwTR32gdStCFky7AeQsyzz9NzfU6WTFCtJPpkddyIx7zn3xMJNBtD7mLArlOTg+rXzIesoNWL6ESJWabAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:14.324748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:addacb381b198e918255313cb1e703883f2fe5d0933e7ac8d06a4337621a4e8e","sha256:a5f2fc2cec6aae0dccca56f61f18b7b98ca594b24b2007e831d0d3b111c6730a"],"state_sha256":"d24188905c96c822f3290e8df1b2cd27b6b20f244715543aaa9f6329b221c271"}