{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CBOCYJSQT5MB7CE4YMM23ZOK7V","short_pith_number":"pith:CBOCYJSQ","canonical_record":{"source":{"id":"1202.0920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T20:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"54add771583789ced784f1da0bdc949597c53ce80c3ac41b5cb3c0cadd9a718d","abstract_canon_sha256":"430b0c54a0745b4f71faa330eadfc94e28713374568fd9adabb8ab379afe52f3"},"schema_version":"1.0"},"canonical_sha256":"105c2c26509f581f889cc319ade5cafd79af38d9801a304d6ad5158e7435f4f2","source":{"kind":"arxiv","id":"1202.0920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0920","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0920v2","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0920","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"CBOCYJSQT5MB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CBOCYJSQT5MB7CE4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CBOCYJSQ","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CBOCYJSQT5MB7CE4YMM23ZOK7V","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T20:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"54add771583789ced784f1da0bdc949597c53ce80c3ac41b5cb3c0cadd9a718d","abstract_canon_sha256":"430b0c54a0745b4f71faa330eadfc94e28713374568fd9adabb8ab379afe52f3"},"schema_version":"1.0"},"canonical_sha256":"105c2c26509f581f889cc319ade5cafd79af38d9801a304d6ad5158e7435f4f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:40.275079Z","signature_b64":"FAGlsJGmNwajPA5mtqhz0593bpiJwF8tkRJBUQtgB8ZVeEVgEqgQmQA3p4ljO+McA/pugTn/GrOMFjK9VH9ACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"105c2c26509f581f889cc319ade5cafd79af38d9801a304d6ad5158e7435f4f2","last_reissued_at":"2026-05-18T03:57:40.274554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:40.274554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0920","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIfDWo7F8FjlON2FCXZgYCEVZfpBJ2efrN3LF3kOvBuSzVCdzA50wHlRIc4Vr2dZlF/2dc3iDrd7Q/Bca231Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:11:52.758370Z"},"content_sha256":"54d371307b0e05ba25fa535d313029a337ea8886f60cfc5e76061c0b60fb80a0","schema_version":"1.0","event_id":"sha256:54d371307b0e05ba25fa535d313029a337ea8886f60cfc5e76061c0b60fb80a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CBOCYJSQT5MB7CE4YMM23ZOK7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The weighted words collector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Dani\\`ele Gardy (PRISM), INRIA Saclay - Ile de France), J\\'er\\'emie Du Boisberranger (PRISM), Yann Ponty (LIX","submitted_at":"2012-02-04T20:33:40Z","abstract_excerpt":"Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this instance of the non-uniform coupon collector lies in the, potentially large, multiplicity of the words/coupons of a given probability/composition. We obtain a general theorem that gives an asymptotic equivalent for the expected waiting time of a general version of the Coupon Collector. This theorem is especially well-suited for classes of coupons featuring high"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0920","kind":"arxiv","version":2},"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":"2026-05-18T03:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4i/TQKEfF36FJrT7i3vgJgiPA8hCA4OIIoZSL+DxbL43RLZanxh7OiPgjTnIcRCwh1SACyt1SpgBAG/+GVoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:11:52.758723Z"},"content_sha256":"ef8de72af90f3936fd8abe804fd9b939c2d29d96d4c53f1f74a01c1f29e776bd","schema_version":"1.0","event_id":"sha256:ef8de72af90f3936fd8abe804fd9b939c2d29d96d4c53f1f74a01c1f29e776bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/bundle.json","state_url":"https://pith.science/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/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":"2026-05-28T02:11:52Z","links":{"resolver":"https://pith.science/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V","bundle":"https://pith.science/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/bundle.json","state":"https://pith.science/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBOCYJSQT5MB7CE4YMM23ZOK7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CBOCYJSQT5MB7CE4YMM23ZOK7V","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":"430b0c54a0745b4f71faa330eadfc94e28713374568fd9adabb8ab379afe52f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T20:33:40Z","title_canon_sha256":"54add771583789ced784f1da0bdc949597c53ce80c3ac41b5cb3c0cadd9a718d"},"schema_version":"1.0","source":{"id":"1202.0920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0920","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0920v2","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0920","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"CBOCYJSQT5MB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CBOCYJSQT5MB7CE4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CBOCYJSQ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:ef8de72af90f3936fd8abe804fd9b939c2d29d96d4c53f1f74a01c1f29e776bd","target":"graph","created_at":"2026-05-18T03:57:40Z","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":"Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this instance of the non-uniform coupon collector lies in the, potentially large, multiplicity of the words/coupons of a given probability/composition. We obtain a general theorem that gives an asymptotic equivalent for the expected waiting time of a general version of the Coupon Collector. This theorem is especially well-suited for classes of coupons featuring high","authors_text":"Dani\\`ele Gardy (PRISM), INRIA Saclay - Ile de France), J\\'er\\'emie Du Boisberranger (PRISM), Yann Ponty (LIX","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T20:33:40Z","title":"The weighted words collector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0920","kind":"arxiv","version":2},"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":"sha256:54d371307b0e05ba25fa535d313029a337ea8886f60cfc5e76061c0b60fb80a0","target":"record","created_at":"2026-05-18T03:57:40Z","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":"430b0c54a0745b4f71faa330eadfc94e28713374568fd9adabb8ab379afe52f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T20:33:40Z","title_canon_sha256":"54add771583789ced784f1da0bdc949597c53ce80c3ac41b5cb3c0cadd9a718d"},"schema_version":"1.0","source":{"id":"1202.0920","kind":"arxiv","version":2}},"canonical_sha256":"105c2c26509f581f889cc319ade5cafd79af38d9801a304d6ad5158e7435f4f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"105c2c26509f581f889cc319ade5cafd79af38d9801a304d6ad5158e7435f4f2","first_computed_at":"2026-05-18T03:57:40.274554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:40.274554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAGlsJGmNwajPA5mtqhz0593bpiJwF8tkRJBUQtgB8ZVeEVgEqgQmQA3p4ljO+McA/pugTn/GrOMFjK9VH9ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:40.275079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54d371307b0e05ba25fa535d313029a337ea8886f60cfc5e76061c0b60fb80a0","sha256:ef8de72af90f3936fd8abe804fd9b939c2d29d96d4c53f1f74a01c1f29e776bd"],"state_sha256":"ef519feaa891fb02f3d893865e4253a1301f97e47ea7ac943dc8af98bcd73c85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3TeZHGopzgl9U3X0zqX297A7ggQtNz9UduHtpAamxcim8zpUfLbICpY7dmnEtCIf/lDB2a+SRZfBvXXWDBPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:11:52.760625Z","bundle_sha256":"9d749178adfbf2da45950c6ce1b8bbc25ce058e583bc7614987973dd123c1b4f"}}