{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ULCCDFWWKKSG4S5R5BO4J7NAC6","short_pith_number":"pith:ULCCDFWW","canonical_record":{"source":{"id":"1706.05250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-16T12:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"dffccf3cc1a70d9748d3bcf552fa352c4cc074c2ef811d28ec20fbcb486a32bc","abstract_canon_sha256":"a6e348fcc97d521c41d1d8e8b921c14d718df064d89addf78684d61af777ad9d"},"schema_version":"1.0"},"canonical_sha256":"a2c42196d652a46e4bb1e85dc4fda017ae77b0e112a98da93f79063c0be25a91","source":{"kind":"arxiv","id":"1706.05250","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ULCCDFWWKKSG4S5R5BO4J7NAC6","target":"record","payload":{"canonical_record":{"source":{"id":"1706.05250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-16T12:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"dffccf3cc1a70d9748d3bcf552fa352c4cc074c2ef811d28ec20fbcb486a32bc","abstract_canon_sha256":"a6e348fcc97d521c41d1d8e8b921c14d718df064d89addf78684d61af777ad9d"},"schema_version":"1.0"},"canonical_sha256":"a2c42196d652a46e4bb1e85dc4fda017ae77b0e112a98da93f79063c0be25a91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:14.324748Z","signature_b64":"FluISwTR32gdStCFky7AeQsyzz9NzfU6WTFCtJPpkddyIx7zn3xMJNBtD7mLArlOTg+rXzIesoNWL6ESJWabAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2c42196d652a46e4bb1e85dc4fda017ae77b0e112a98da93f79063c0be25a91","last_reissued_at":"2026-05-18T00:42:14.323998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:14.323998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.05250","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wAEwJaUE9fCzwMozE/pe/X24QknzlLDaaaFPcNIcAHT0QQD+WKOp1sk+CpxgWgTVSi//Hz4KW3OQ4CviUNvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:52:01.544360Z"},"content_sha256":"addacb381b198e918255313cb1e703883f2fe5d0933e7ac8d06a4337621a4e8e","schema_version":"1.0","event_id":"sha256:addacb381b198e918255313cb1e703883f2fe5d0933e7ac8d06a4337621a4e8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ULCCDFWWKKSG4S5R5BO4J7NAC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contributions to the Generalized Coupon Collector and LRU Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Christian Berthet","submitted_at":"2017-06-16T12:39:23Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05250","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"udVaILxRO/3xIukRDYDIZNn0P4ORIq8cu0X+ldyvTfnRjVY+nHUttSnRdZI/JmkhoVGnksJ1+8XMgeL0H7EiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:52:01.544700Z"},"content_sha256":"a5f2fc2cec6aae0dccca56f61f18b7b98ca594b24b2007e831d0d3b111c6730a","schema_version":"1.0","event_id":"sha256:a5f2fc2cec6aae0dccca56f61f18b7b98ca594b24b2007e831d0d3b111c6730a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/bundle.json","state_url":"https://pith.science/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T12:52:01Z","links":{"resolver":"https://pith.science/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6","bundle":"https://pith.science/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/bundle.json","state":"https://pith.science/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULCCDFWWKKSG4S5R5BO4J7NAC6/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UO8m5y3RtDnWdo48zpNKD6yGfBI1M/vUFjcbqGoW+5TvYHm7KvXXG/Rkl6sc8OYMsoDtQgrjjV4uzFxwXn2VAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T12:52:01.546638Z","bundle_sha256":"182d3819dd0383663519f83d4418069a5c88cdf319943a30224c4e5b4c0c8192"}}