{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2XGAPHZZA5HMENXT3YNJSP5WSH","short_pith_number":"pith:2XGAPHZZ","canonical_record":{"source":{"id":"1507.08119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T12:43:09Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6b247e1c6b1d92101b60ebd90f7d05240e60d929afea68eff506963ad7b8457d","abstract_canon_sha256":"e31f143dd26770664c73ce0082c436cb891f1cc72929934a39ae9d9fc5f0e41d"},"schema_version":"1.0"},"canonical_sha256":"d5cc079f39074ec236f3de1a993fb691c9306ded9ab75d6565c8738b546a8c09","source":{"kind":"arxiv","id":"1507.08119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08119","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08119v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08119","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"2XGAPHZZA5HM","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2XGAPHZZA5HMENXT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2XGAPHZZ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2XGAPHZZA5HMENXT3YNJSP5WSH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T12:43:09Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6b247e1c6b1d92101b60ebd90f7d05240e60d929afea68eff506963ad7b8457d","abstract_canon_sha256":"e31f143dd26770664c73ce0082c436cb891f1cc72929934a39ae9d9fc5f0e41d"},"schema_version":"1.0"},"canonical_sha256":"d5cc079f39074ec236f3de1a993fb691c9306ded9ab75d6565c8738b546a8c09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:08.284161Z","signature_b64":"0eu78pZQHEyqRUOOAqTdACeaaZ2lpxi3Rx3hdPwg0tL/vs3uRQeUriLgaPc/3ZzN3rHEwXSg/uUGC7Tck1GABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5cc079f39074ec236f3de1a993fb691c9306ded9ab75d6565c8738b546a8c09","last_reissued_at":"2026-05-18T01:36:08.283669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:08.283669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08119","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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bSj+4qD9jXtH0vdHTwIGSDHH7XH476VD8LjTMoujdOlOFLQK0jB9nFN8RRmeNoLfXjk7FDWbqbDibzKJXm9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:52:11.487328Z"},"content_sha256":"27452456a75b5d5eb664c7ab0a31902a533be6da19d54e32f1452c43fb62e1f2","schema_version":"1.0","event_id":"sha256:27452456a75b5d5eb664c7ab0a31902a533be6da19d54e32f1452c43fb62e1f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2XGAPHZZA5HMENXT3YNJSP5WSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The CLT Analogue for Cyclic Urns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.PR","authors_text":"Noela S. M\\\"uller, Ralph Neininger","submitted_at":"2015-07-29T12:43:09Z","abstract_excerpt":"A cyclic urn is an urn model for balls of types $0,\\ldots,m-1$ where in each draw the ball drawn, say of type $j$, is returned to the urn together with a new ball of type $j+1 \\mod m$. The case $m=2$ is the well-known Friedman urn. The composition vector, i.e., the vector of the numbers of balls of each type after $n$ steps is, after normalization, known to be asymptotically normal for $2\\le m\\le 6$. For $m\\ge 7$ the normalized composition vector does not converge. However, there is an almost sure approximation by a periodic random vector. In this paper the asymptotic fluctuations around this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08119","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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvfNz03y7ybDzXOHj/vtjcVNw+fEVJDdGGbSVwo4lFqZNotb0eidm0CRfnyJqavTrw0DnpksInolMuo5Dw2mCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:52:11.487687Z"},"content_sha256":"6c8e43574b576a906855dc46b1c2b58486d48bbc503234e908f319699507fc29","schema_version":"1.0","event_id":"sha256:6c8e43574b576a906855dc46b1c2b58486d48bbc503234e908f319699507fc29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/bundle.json","state_url":"https://pith.science/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/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":"2026-06-06T16:52:11Z","links":{"resolver":"https://pith.science/pith/2XGAPHZZA5HMENXT3YNJSP5WSH","bundle":"https://pith.science/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/bundle.json","state":"https://pith.science/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2XGAPHZZA5HMENXT3YNJSP5WSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2XGAPHZZA5HMENXT3YNJSP5WSH","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":"e31f143dd26770664c73ce0082c436cb891f1cc72929934a39ae9d9fc5f0e41d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T12:43:09Z","title_canon_sha256":"6b247e1c6b1d92101b60ebd90f7d05240e60d929afea68eff506963ad7b8457d"},"schema_version":"1.0","source":{"id":"1507.08119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08119","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08119v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08119","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"2XGAPHZZA5HM","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2XGAPHZZA5HMENXT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2XGAPHZZ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:6c8e43574b576a906855dc46b1c2b58486d48bbc503234e908f319699507fc29","target":"graph","created_at":"2026-05-18T01:36:08Z","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":"A cyclic urn is an urn model for balls of types $0,\\ldots,m-1$ where in each draw the ball drawn, say of type $j$, is returned to the urn together with a new ball of type $j+1 \\mod m$. The case $m=2$ is the well-known Friedman urn. The composition vector, i.e., the vector of the numbers of balls of each type after $n$ steps is, after normalization, known to be asymptotically normal for $2\\le m\\le 6$. For $m\\ge 7$ the normalized composition vector does not converge. However, there is an almost sure approximation by a periodic random vector. In this paper the asymptotic fluctuations around this ","authors_text":"Noela S. M\\\"uller, Ralph Neininger","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T12:43:09Z","title":"The CLT Analogue for Cyclic Urns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08119","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":"sha256:27452456a75b5d5eb664c7ab0a31902a533be6da19d54e32f1452c43fb62e1f2","target":"record","created_at":"2026-05-18T01:36:08Z","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":"e31f143dd26770664c73ce0082c436cb891f1cc72929934a39ae9d9fc5f0e41d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T12:43:09Z","title_canon_sha256":"6b247e1c6b1d92101b60ebd90f7d05240e60d929afea68eff506963ad7b8457d"},"schema_version":"1.0","source":{"id":"1507.08119","kind":"arxiv","version":1}},"canonical_sha256":"d5cc079f39074ec236f3de1a993fb691c9306ded9ab75d6565c8738b546a8c09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5cc079f39074ec236f3de1a993fb691c9306ded9ab75d6565c8738b546a8c09","first_computed_at":"2026-05-18T01:36:08.283669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:08.283669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0eu78pZQHEyqRUOOAqTdACeaaZ2lpxi3Rx3hdPwg0tL/vs3uRQeUriLgaPc/3ZzN3rHEwXSg/uUGC7Tck1GABw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:08.284161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27452456a75b5d5eb664c7ab0a31902a533be6da19d54e32f1452c43fb62e1f2","sha256:6c8e43574b576a906855dc46b1c2b58486d48bbc503234e908f319699507fc29"],"state_sha256":"1e13257c84ed886ce52afa028294aecc14752f522b352c833bf26932aa6a9872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmhkw+Sn3qxHaQU8JvYLsw66lZNm2nRAUZLgvFl8k2COhXbJ75ltqlole6O8ptFqSZWxXVHfKGlJZIxocSlaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:52:11.489770Z","bundle_sha256":"86b779b3b28c31200eccff3460262f0aa6a1e29c2c4eec94b9262ce897352955"}}