{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VWXZW4CX5QUHKBXOCTSJVMSOFE","short_pith_number":"pith:VWXZW4CX","canonical_record":{"source":{"id":"2607.23401","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-26T00:42:44Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"4795daba119b51582138f27edfd8b02d3bb7566fe9103064fdba930b118607a5","abstract_canon_sha256":"cb4bbd0e9f200fc44c279a9795c62a35754632ed231173d012c2fd3733446bf2"},"schema_version":"1.0"},"canonical_sha256":"adaf9b7057ec287506ee14e49ab24e291b5e11b4682163300a67924973b49c2c","source":{"kind":"arxiv","id":"2607.23401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23401","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23401v1","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23401","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"VWXZW4CX5QUH","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"VWXZW4CX5QUHKBXO","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"VWXZW4CX","created_at":"2026-07-28T01:22:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VWXZW4CX5QUHKBXOCTSJVMSOFE","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23401","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-26T00:42:44Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"4795daba119b51582138f27edfd8b02d3bb7566fe9103064fdba930b118607a5","abstract_canon_sha256":"cb4bbd0e9f200fc44c279a9795c62a35754632ed231173d012c2fd3733446bf2"},"schema_version":"1.0"},"canonical_sha256":"adaf9b7057ec287506ee14e49ab24e291b5e11b4682163300a67924973b49c2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:51.306459Z","signature_b64":"t+HkumMUUjVlKoaKeLFomLnesi0WL1ufFTVBqdp/RQOu4XBOhOse+pi8pAGpY7b2l/l4JiqtR1m0/QWLHxS3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adaf9b7057ec287506ee14e49ab24e291b5e11b4682163300a67924973b49c2c","last_reissued_at":"2026-07-28T01:22:51.305690Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:51.305690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23401","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":"2026-07-28T01:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IkXX8vp6a0DFc1t+pTZZcci2DhMFf7RhpGkN7fAKVqJHxMJGnUbAuiJOTyahZHuein0cYgAoMKOBPUmqrosCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:24:05.649512Z"},"content_sha256":"724e88bc53e21857f76d342e1843b94fe080bc4093a2f65556280870afd5d2c8","schema_version":"1.0","event_id":"sha256:724e88bc53e21857f76d342e1843b94fe080bc4093a2f65556280870afd5d2c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VWXZW4CX5QUHKBXOCTSJVMSOFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Theorems for the Pitman-Yor Frequency Spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"math.PR","authors_text":"Ross Arthur Maller, Soudabeh Shemehsavar","submitted_at":"2026-07-26T00:42:44Z","abstract_excerpt":"We derive a general distribution formula applicable to a wide variety of Gibbs-type partitions and use it to obtain large sample results for linear combinations of the component frequency spectrum $(M_{jn})_{1\\le j\\le n}$ (in genetics, the allele frequency spectrum) associated with a random partitioning of $\\{1,2,\\ldots, n\\}$. The two-parameter Pitman-Yor sampling model is analysed in detail and asymptotic distributions of sums of the form $\\sum _{j=\\lf \\lambda n\\rf}^{\\lf \\mu n\\rf} M_{jn}$, $0<\\lambda\\le \\mu\\le 1$, are obtained. Our results suggest a possible functional limit theorem for $\\sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-28T01:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LoV/5VCtjfbsH2xH2vFO3Wyx5OglsGE+aKKr69/2uPYNbbFsxyADHgTbA1ByfLwlN+JvBH6lAYt0Oc4HMpBZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:24:05.650018Z"},"content_sha256":"1ee09bbdd2400dfa3c1388ef3b4c787f378f5ff6a1941c41d28c2fd06b366061","schema_version":"1.0","event_id":"sha256:1ee09bbdd2400dfa3c1388ef3b4c787f378f5ff6a1941c41d28c2fd06b366061"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/bundle.json","state_url":"https://pith.science/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/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":"2026-08-03T21:24:05Z","links":{"resolver":"https://pith.science/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE","bundle":"https://pith.science/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/bundle.json","state":"https://pith.science/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWXZW4CX5QUHKBXOCTSJVMSOFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VWXZW4CX5QUHKBXOCTSJVMSOFE","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":"cb4bbd0e9f200fc44c279a9795c62a35754632ed231173d012c2fd3733446bf2","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-26T00:42:44Z","title_canon_sha256":"4795daba119b51582138f27edfd8b02d3bb7566fe9103064fdba930b118607a5"},"schema_version":"1.0","source":{"id":"2607.23401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23401","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23401v1","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23401","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"VWXZW4CX5QUH","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"VWXZW4CX5QUHKBXO","created_at":"2026-07-28T01:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"VWXZW4CX","created_at":"2026-07-28T01:22:51Z"}],"graph_snapshots":[{"event_id":"sha256:1ee09bbdd2400dfa3c1388ef3b4c787f378f5ff6a1941c41d28c2fd06b366061","target":"graph","created_at":"2026-07-28T01:22:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.23401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a general distribution formula applicable to a wide variety of Gibbs-type partitions and use it to obtain large sample results for linear combinations of the component frequency spectrum $(M_{jn})_{1\\le j\\le n}$ (in genetics, the allele frequency spectrum) associated with a random partitioning of $\\{1,2,\\ldots, n\\}$. The two-parameter Pitman-Yor sampling model is analysed in detail and asymptotic distributions of sums of the form $\\sum _{j=\\lf \\lambda n\\rf}^{\\lf \\mu n\\rf} M_{jn}$, $0<\\lambda\\le \\mu\\le 1$, are obtained. Our results suggest a possible functional limit theorem for $\\sum","authors_text":"Ross Arthur Maller, Soudabeh Shemehsavar","cross_cats":["math.ST","stat.ME","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-26T00:42:44Z","title":"Limit Theorems for the Pitman-Yor Frequency Spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23401","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":"sha256:724e88bc53e21857f76d342e1843b94fe080bc4093a2f65556280870afd5d2c8","target":"record","created_at":"2026-07-28T01:22:51Z","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":"cb4bbd0e9f200fc44c279a9795c62a35754632ed231173d012c2fd3733446bf2","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-26T00:42:44Z","title_canon_sha256":"4795daba119b51582138f27edfd8b02d3bb7566fe9103064fdba930b118607a5"},"schema_version":"1.0","source":{"id":"2607.23401","kind":"arxiv","version":1}},"canonical_sha256":"adaf9b7057ec287506ee14e49ab24e291b5e11b4682163300a67924973b49c2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adaf9b7057ec287506ee14e49ab24e291b5e11b4682163300a67924973b49c2c","first_computed_at":"2026-07-28T01:22:51.305690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:51.305690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+HkumMUUjVlKoaKeLFomLnesi0WL1ufFTVBqdp/RQOu4XBOhOse+pi8pAGpY7b2l/l4JiqtR1m0/QWLHxS3Dw==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:51.306459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:724e88bc53e21857f76d342e1843b94fe080bc4093a2f65556280870afd5d2c8","sha256:1ee09bbdd2400dfa3c1388ef3b4c787f378f5ff6a1941c41d28c2fd06b366061"],"state_sha256":"f34d81f9fcdd21c331b6d0a7997a7bdf85f829f2255841e335697ccf7c4efc81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73fMxl18oKQK5ALgqeGvufzNVJyVz+fK8s8hFxBCvGH8Qlyh6u4jvrD4/IM9fw9XNSa4PdFOJ7gDU8cTbW4QAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:24:05.654771Z","bundle_sha256":"6bb1ad9d7afcecf381f47228b4b291971e340b17fa829ebc8b59a1345024238c"}}