{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:HBWHZ5SEGVEYPLHIEZAQFXS2XJ","short_pith_number":"pith:HBWHZ5SE","canonical_record":{"source":{"id":"math/0110181","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-10-17T17:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"c530d9c3e82f288d33a1ce84a2821b2010697a40a52925a96c7a87260ec725b0","abstract_canon_sha256":"64db4d9b17bc3ba3197b74e02df00d2b801890e9e7c6df55239213e94a6ec1df"},"schema_version":"1.0"},"canonical_sha256":"386c7cf644354987ace8264102de5aba6e5b6db2843eae83771af9a849b32678","source":{"kind":"arxiv","id":"math/0110181","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110181","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110181v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110181","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"HBWHZ5SEGVEY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"HBWHZ5SEGVEYPLHI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"HBWHZ5SE","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:HBWHZ5SEGVEYPLHIEZAQFXS2XJ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0110181","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-10-17T17:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"c530d9c3e82f288d33a1ce84a2821b2010697a40a52925a96c7a87260ec725b0","abstract_canon_sha256":"64db4d9b17bc3ba3197b74e02df00d2b801890e9e7c6df55239213e94a6ec1df"},"schema_version":"1.0"},"canonical_sha256":"386c7cf644354987ace8264102de5aba6e5b6db2843eae83771af9a849b32678","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.805707Z","signature_b64":"LYkgBUSWbORZRJiPzotJ1uCIBmUPSxKjqYlg8pWLb771gcbHlbuCReI1P/u4QEF0ZDnTXTrbHwblzfysMCstDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"386c7cf644354987ace8264102de5aba6e5b6db2843eae83771af9a849b32678","last_reissued_at":"2026-05-18T01:38:29.805244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.805244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0110181","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bIUoYPuIQRJ7SOummysURDGg5QbflVTe91if47bNgiTqjuLnMxKOt7EmW8iLFagWzAd7SGGB+kWq03dCeoypBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:36.918371Z"},"content_sha256":"7fb97f06e0d7d5eeb49286e4a3d690f08422eb0391f227fee270fe98a0c1fd55","schema_version":"1.0","event_id":"sha256:7fb97f06e0d7d5eeb49286e4a3d690f08422eb0391f227fee270fe98a0c1fd55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:HBWHZ5SEGVEYPLHIEZAQFXS2XJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generatingfunctionology approach to a problem of Wilf","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla D. Savage, Cecil C. Rousseau, Pawel Hitczenko","submitted_at":"2001-10-17T17:21:11Z","abstract_excerpt":"Wilf posed the following problem: determine asymptotically as $n\\to\\infty$ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem was given by Hitczenko and Savage. In this paper, we study this question using the techniques of generating functions and singularity analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110181","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TT1OfbGiEsgKqk0j/HNxLaKIL9xeD1AB8M4tuPPwMVJybuxoeKDhaq9y5i6J1eM5Rro6TwKu1O28TpAqaauCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:36.918737Z"},"content_sha256":"eabdbf3f552f3f6a1c708b636162e062a91936a9b4b6ef369077bf495e5cec5f","schema_version":"1.0","event_id":"sha256:eabdbf3f552f3f6a1c708b636162e062a91936a9b4b6ef369077bf495e5cec5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/bundle.json","state_url":"https://pith.science/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/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":"2026-06-02T13:17:36Z","links":{"resolver":"https://pith.science/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ","bundle":"https://pith.science/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/bundle.json","state":"https://pith.science/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBWHZ5SEGVEYPLHIEZAQFXS2XJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:HBWHZ5SEGVEYPLHIEZAQFXS2XJ","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":"64db4d9b17bc3ba3197b74e02df00d2b801890e9e7c6df55239213e94a6ec1df","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2001-10-17T17:21:11Z","title_canon_sha256":"c530d9c3e82f288d33a1ce84a2821b2010697a40a52925a96c7a87260ec725b0"},"schema_version":"1.0","source":{"id":"math/0110181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110181","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110181v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110181","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"HBWHZ5SEGVEY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"HBWHZ5SEGVEYPLHI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"HBWHZ5SE","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:eabdbf3f552f3f6a1c708b636162e062a91936a9b4b6ef369077bf495e5cec5f","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"Wilf posed the following problem: determine asymptotically as $n\\to\\infty$ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem was given by Hitczenko and Savage. In this paper, we study this question using the techniques of generating functions and singularity analysis.","authors_text":"Carla D. Savage, Cecil C. Rousseau, Pawel Hitczenko","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2001-10-17T17:21:11Z","title":"A generatingfunctionology approach to a problem of Wilf"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110181","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":"sha256:7fb97f06e0d7d5eeb49286e4a3d690f08422eb0391f227fee270fe98a0c1fd55","target":"record","created_at":"2026-05-18T01:38:29Z","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":"64db4d9b17bc3ba3197b74e02df00d2b801890e9e7c6df55239213e94a6ec1df","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2001-10-17T17:21:11Z","title_canon_sha256":"c530d9c3e82f288d33a1ce84a2821b2010697a40a52925a96c7a87260ec725b0"},"schema_version":"1.0","source":{"id":"math/0110181","kind":"arxiv","version":1}},"canonical_sha256":"386c7cf644354987ace8264102de5aba6e5b6db2843eae83771af9a849b32678","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"386c7cf644354987ace8264102de5aba6e5b6db2843eae83771af9a849b32678","first_computed_at":"2026-05-18T01:38:29.805244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.805244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LYkgBUSWbORZRJiPzotJ1uCIBmUPSxKjqYlg8pWLb771gcbHlbuCReI1P/u4QEF0ZDnTXTrbHwblzfysMCstDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.805707Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fb97f06e0d7d5eeb49286e4a3d690f08422eb0391f227fee270fe98a0c1fd55","sha256:eabdbf3f552f3f6a1c708b636162e062a91936a9b4b6ef369077bf495e5cec5f"],"state_sha256":"8978c91cac421f7dec2359423a5dfd6f3db0d86508680a3b135e9dea9db130b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pnCUggOy87SGjEB4nvW5Vj6sMXKnx5Gs47p/HejhlcYA9yYOH0UgZCh2kEQXNyIW3bCYkQmWvkAbBilcUX4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:17:36.921138Z","bundle_sha256":"ea2ced4bbb53037c86e251e6946911fbce37c2f4970fabfa24e6452d02f35955"}}