{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:G2IIMNLI5JRDIES53GMEVCDOHM","short_pith_number":"pith:G2IIMNLI","canonical_record":{"source":{"id":"1703.01886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-06T14:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"552ea9b31f2aa19440d5e474de22faa5d65cf6170450b42aa1efd033fa92952a","abstract_canon_sha256":"49aac582801fd3ae738ef090fb9f41750f1cb34af9833247cf1622ec4aab2922"},"schema_version":"1.0"},"canonical_sha256":"3690863568ea6234125dd9984a886e3b11ca79f16a5be78ea1fefe17ec849797","source":{"kind":"arxiv","id":"1703.01886","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01886","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01886v1","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01886","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"G2IIMNLI5JRD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2IIMNLI5JRDIES5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2IIMNLI","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:G2IIMNLI5JRDIES53GMEVCDOHM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-06T14:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"552ea9b31f2aa19440d5e474de22faa5d65cf6170450b42aa1efd033fa92952a","abstract_canon_sha256":"49aac582801fd3ae738ef090fb9f41750f1cb34af9833247cf1622ec4aab2922"},"schema_version":"1.0"},"canonical_sha256":"3690863568ea6234125dd9984a886e3b11ca79f16a5be78ea1fefe17ec849797","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:29.392688Z","signature_b64":"P2VV+JfHjU8B6UEJKjl68J+sK5ElFYe7UZ5vvf+Rsgf0tPalWwv+W7bRbMu5qZ5DljCn5H8Cc8CTJFQ3NV+iBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3690863568ea6234125dd9984a886e3b11ca79f16a5be78ea1fefe17ec849797","last_reissued_at":"2026-05-18T00:49:29.391967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:29.391967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01886","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":"2026-05-18T00:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j1TKda5zh9Fn3uDpGw2VsBuiVaxcuX7+C8mxtMfaksGHgni26/srE7kOP8GLfLEwpxQo5/tbxVDn9pOTzbkYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:53:32.222306Z"},"content_sha256":"8918c596c9b485470ff88f7d0e9d52cb08e53ed5c7a9d71c8acbf33410d5b2e9","schema_version":"1.0","event_id":"sha256:8918c596c9b485470ff88f7d0e9d52cb08e53ed5c7a9d71c8acbf33410d5b2e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:G2IIMNLI5JRDIES53GMEVCDOHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Von Schelling Formula for the Generalized Coupon Collector Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Christian Berthet","submitted_at":"2017-03-06T14:15:29Z","abstract_excerpt":"This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of powers of subset probabilities which to our knowledge is new. A set of binomial coefficients is used as a basis for decomposition of these sums of powers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01886","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":"2026-05-18T00:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4oMDxarcxuShWHyfGmYDTmGCIJiIvu5xuF8hYxWvwpQ3NYcIDwAKvQQyVgiAq7ig6V6pLnW79FLzE9tcUURBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:53:32.222665Z"},"content_sha256":"8e394d0b459690c230cb22bc0b46ea4ae9ba91cfe435c388f9847fac894ecaf6","schema_version":"1.0","event_id":"sha256:8e394d0b459690c230cb22bc0b46ea4ae9ba91cfe435c388f9847fac894ecaf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2IIMNLI5JRDIES53GMEVCDOHM/bundle.json","state_url":"https://pith.science/pith/G2IIMNLI5JRDIES53GMEVCDOHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2IIMNLI5JRDIES53GMEVCDOHM/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":"2026-07-03T13:53:32Z","links":{"resolver":"https://pith.science/pith/G2IIMNLI5JRDIES53GMEVCDOHM","bundle":"https://pith.science/pith/G2IIMNLI5JRDIES53GMEVCDOHM/bundle.json","state":"https://pith.science/pith/G2IIMNLI5JRDIES53GMEVCDOHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2IIMNLI5JRDIES53GMEVCDOHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G2IIMNLI5JRDIES53GMEVCDOHM","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":"49aac582801fd3ae738ef090fb9f41750f1cb34af9833247cf1622ec4aab2922","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-06T14:15:29Z","title_canon_sha256":"552ea9b31f2aa19440d5e474de22faa5d65cf6170450b42aa1efd033fa92952a"},"schema_version":"1.0","source":{"id":"1703.01886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01886","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01886v1","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01886","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"G2IIMNLI5JRD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2IIMNLI5JRDIES5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2IIMNLI","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:8e394d0b459690c230cb22bc0b46ea4ae9ba91cfe435c388f9847fac894ecaf6","target":"graph","created_at":"2026-05-18T00:49:29Z","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":"This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of powers of subset probabilities which to our knowledge is new. A set of binomial coefficients is used as a basis for decomposition of these sums of powers.","authors_text":"Christian Berthet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-06T14:15:29Z","title":"On Von Schelling Formula for the Generalized Coupon Collector Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01886","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":"sha256:8918c596c9b485470ff88f7d0e9d52cb08e53ed5c7a9d71c8acbf33410d5b2e9","target":"record","created_at":"2026-05-18T00:49:29Z","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":"49aac582801fd3ae738ef090fb9f41750f1cb34af9833247cf1622ec4aab2922","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-06T14:15:29Z","title_canon_sha256":"552ea9b31f2aa19440d5e474de22faa5d65cf6170450b42aa1efd033fa92952a"},"schema_version":"1.0","source":{"id":"1703.01886","kind":"arxiv","version":1}},"canonical_sha256":"3690863568ea6234125dd9984a886e3b11ca79f16a5be78ea1fefe17ec849797","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3690863568ea6234125dd9984a886e3b11ca79f16a5be78ea1fefe17ec849797","first_computed_at":"2026-05-18T00:49:29.391967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:29.391967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P2VV+JfHjU8B6UEJKjl68J+sK5ElFYe7UZ5vvf+Rsgf0tPalWwv+W7bRbMu5qZ5DljCn5H8Cc8CTJFQ3NV+iBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:29.392688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8918c596c9b485470ff88f7d0e9d52cb08e53ed5c7a9d71c8acbf33410d5b2e9","sha256:8e394d0b459690c230cb22bc0b46ea4ae9ba91cfe435c388f9847fac894ecaf6"],"state_sha256":"e71a2cf9924a72faa0b3dd09f1420746c77d213dce02aa8bf7652560946298ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i65gCK79YHoNf2+3m5GuJ+1iFTFqJRtkdFjthk4t0WrypGuR7HfKZ+bLpFKvyBf+K+AY2FjC5PNTV1sL/fm2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:53:32.224501Z","bundle_sha256":"246f80c86499b0eec0174851ab5be408b698d689d89b7d0ac62ffc3a38db81ef"}}