{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JOAIEFOIQNZEZAUNJYLST2HWBI","short_pith_number":"pith:JOAIEFOI","canonical_record":{"source":{"id":"1302.1412","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-06T15:51:55Z","cross_cats_sorted":[],"title_canon_sha256":"5651d8025e0279109dde7a39cbf2681b9d600b0266333eecbc972bf7fbc91291","abstract_canon_sha256":"60238cb21bdbdd6850e962a5ab3082d424097d9724b2bac0c0c9e2afe51a68fd"},"schema_version":"1.0"},"canonical_sha256":"4b808215c883724c828d4e1729e8f60a16ae5de9ad91da93082173d77bde6a99","source":{"kind":"arxiv","id":"1302.1412","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1412","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1412v3","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1412","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"JOAIEFOIQNZE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JOAIEFOIQNZEZAUN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JOAIEFOI","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JOAIEFOIQNZEZAUNJYLST2HWBI","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1412","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-06T15:51:55Z","cross_cats_sorted":[],"title_canon_sha256":"5651d8025e0279109dde7a39cbf2681b9d600b0266333eecbc972bf7fbc91291","abstract_canon_sha256":"60238cb21bdbdd6850e962a5ab3082d424097d9724b2bac0c0c9e2afe51a68fd"},"schema_version":"1.0"},"canonical_sha256":"4b808215c883724c828d4e1729e8f60a16ae5de9ad91da93082173d77bde6a99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:17.094070Z","signature_b64":"ppHk3asJ3e5XFFmIYRKy9UM17klwo+eGVBM9gZIAg2OwjrNpkovh1NwZUOu/l2k95vfOW5DzyMBbInvYyVRsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b808215c883724c828d4e1729e8f60a16ae5de9ad91da93082173d77bde6a99","last_reissued_at":"2026-05-18T03:22:17.093671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:17.093671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1412","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qI68nR0QxANdT1G/1Wjq2zONDt7hImUFr5xNCSXJi8yv2aV80tipVFFbW/pNIv6lF+RyA/CBW7+IzLzOdOGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:53:59.764651Z"},"content_sha256":"8da3b4884cabbd296214ffc5cf23d4555d2efe755f318039d4a872134a9f291c","schema_version":"1.0","event_id":"sha256:8da3b4884cabbd296214ffc5cf23d4555d2efe755f318039d4a872134a9f291c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JOAIEFOIQNZEZAUNJYLST2HWBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothing equations for large P\\'olya urns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brigitte Chauvin, C\\'ecile Mailler, Nicolas Pouyanne","submitted_at":"2013-02-06T15:51:55Z","abstract_excerpt":"Consider a balanced non triangular two-color P\\'olya-Eggenberger urn process, assumed to be large which means that the ratio sigma of the replacement matrix eigenvalues satisfies 1/2<sigma <1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second principal direction, this random vector admits also an almost sure asymptotics and a real-valued limit random variable arises, named WDT in discrete time and WCT in continous time. The paper deals with the distributions of both W. Appe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1412","kind":"arxiv","version":3},"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":"2026-05-18T03:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zShDgnUx+o9IxSYvGnllQU7PrQdTO1PP7zBF0avqULmDbHoc1EXqY5DVhlIrc5RQWfnWbyFEHspXXCe2uf9DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:53:59.765302Z"},"content_sha256":"5a4c865c5a020026a75fc2d208f1ff6a6e2426235d68d38afa113de8d037ab23","schema_version":"1.0","event_id":"sha256:5a4c865c5a020026a75fc2d208f1ff6a6e2426235d68d38afa113de8d037ab23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/bundle.json","state_url":"https://pith.science/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/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":"2026-05-29T21:53:59Z","links":{"resolver":"https://pith.science/pith/JOAIEFOIQNZEZAUNJYLST2HWBI","bundle":"https://pith.science/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/bundle.json","state":"https://pith.science/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOAIEFOIQNZEZAUNJYLST2HWBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JOAIEFOIQNZEZAUNJYLST2HWBI","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":"60238cb21bdbdd6850e962a5ab3082d424097d9724b2bac0c0c9e2afe51a68fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-06T15:51:55Z","title_canon_sha256":"5651d8025e0279109dde7a39cbf2681b9d600b0266333eecbc972bf7fbc91291"},"schema_version":"1.0","source":{"id":"1302.1412","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1412","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1412v3","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1412","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"JOAIEFOIQNZE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JOAIEFOIQNZEZAUN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JOAIEFOI","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:5a4c865c5a020026a75fc2d208f1ff6a6e2426235d68d38afa113de8d037ab23","target":"graph","created_at":"2026-05-18T03:22:17Z","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":"Consider a balanced non triangular two-color P\\'olya-Eggenberger urn process, assumed to be large which means that the ratio sigma of the replacement matrix eigenvalues satisfies 1/2<sigma <1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second principal direction, this random vector admits also an almost sure asymptotics and a real-valued limit random variable arises, named WDT in discrete time and WCT in continous time. The paper deals with the distributions of both W. Appe","authors_text":"Brigitte Chauvin, C\\'ecile Mailler, Nicolas Pouyanne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-06T15:51:55Z","title":"Smoothing equations for large P\\'olya urns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1412","kind":"arxiv","version":3},"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":"sha256:8da3b4884cabbd296214ffc5cf23d4555d2efe755f318039d4a872134a9f291c","target":"record","created_at":"2026-05-18T03:22:17Z","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":"60238cb21bdbdd6850e962a5ab3082d424097d9724b2bac0c0c9e2afe51a68fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-06T15:51:55Z","title_canon_sha256":"5651d8025e0279109dde7a39cbf2681b9d600b0266333eecbc972bf7fbc91291"},"schema_version":"1.0","source":{"id":"1302.1412","kind":"arxiv","version":3}},"canonical_sha256":"4b808215c883724c828d4e1729e8f60a16ae5de9ad91da93082173d77bde6a99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b808215c883724c828d4e1729e8f60a16ae5de9ad91da93082173d77bde6a99","first_computed_at":"2026-05-18T03:22:17.093671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:17.093671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ppHk3asJ3e5XFFmIYRKy9UM17klwo+eGVBM9gZIAg2OwjrNpkovh1NwZUOu/l2k95vfOW5DzyMBbInvYyVRsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:17.094070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1412","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da3b4884cabbd296214ffc5cf23d4555d2efe755f318039d4a872134a9f291c","sha256:5a4c865c5a020026a75fc2d208f1ff6a6e2426235d68d38afa113de8d037ab23"],"state_sha256":"33bdd1ffd172a37cf4a28fe90476f0211e7b7d24f4251336d9e2b17d99ceb95c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtYzqzdQFe3G3UyLv82XIgVsK1fc8qLpZJrVFsHuddt00PuO9ZbZkGKzqZYrfuTCd7qEbEGW679UKzz6ujLrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T21:53:59.768623Z","bundle_sha256":"480fd7783c544144dae33fafc93f29f946a7411d9966d16e3bb4134ea76abc69"}}