{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FHIR543HEKYTRFRDR54ZGGW7V5","short_pith_number":"pith:FHIR543H","canonical_record":{"source":{"id":"2408.06611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-13T03:48:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0b507476f8800861e3d77125c51307e28efdaac759a7aa1def14f6b3c2a2d965","abstract_canon_sha256":"fa33ddd264fdcfd6e3036342b92bd428ebab54477280045382f051dad02bc58f"},"schema_version":"1.0"},"canonical_sha256":"29d11ef36722b13896238f79931adfaf4f69f8fa565724bf9f45263b68ae3918","source":{"kind":"arxiv","id":"2408.06611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.06611","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2408.06611v2","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.06611","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"FHIR543HEKYT","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"FHIR543HEKYTRFRD","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"FHIR543H","created_at":"2026-07-05T10:54:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FHIR543HEKYTRFRDR54ZGGW7V5","target":"record","payload":{"canonical_record":{"source":{"id":"2408.06611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-13T03:48:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0b507476f8800861e3d77125c51307e28efdaac759a7aa1def14f6b3c2a2d965","abstract_canon_sha256":"fa33ddd264fdcfd6e3036342b92bd428ebab54477280045382f051dad02bc58f"},"schema_version":"1.0"},"canonical_sha256":"29d11ef36722b13896238f79931adfaf4f69f8fa565724bf9f45263b68ae3918","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:35.398675Z","signature_b64":"saxzfz7va/CcOdjIn9barxhCDUEjIdv2S7BZuktdrnHqPHLwZ1fC5fbt8jJ801+lioaLhzduIKwnX6Pfv+RECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29d11ef36722b13896238f79931adfaf4f69f8fa565724bf9f45263b68ae3918","last_reissued_at":"2026-07-05T10:54:35.398140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:35.398140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.06611","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":"2026-07-05T10:54:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iFZpP6WdEIa3z/usOv5Mivbbs4xesvF22cfXG80zzvRIlKedOVYN8QOz+geV6WfoEUCXDndQVl/UP+UB/N49Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:20:31.853440Z"},"content_sha256":"ff5779ae7417b450550539cf3215fdd6184e2b67af0761f2fd962f5051218f93","schema_version":"1.0","event_id":"sha256:ff5779ae7417b450550539cf3215fdd6184e2b67af0761f2fd962f5051218f93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FHIR543HEKYTRFRDR54ZGGW7V5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson approximation for large permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Nathan Tung, Persi Diaconis","submitted_at":"2024-08-13T03:48:15Z","abstract_excerpt":"Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of $G_{k,n}$. This includes novel limit theorems for fixed points, cycles of various lengths, number of cycles and inversions. The limits are compound Poisson distributions with interesting dependence structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06611","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.06611/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":"2026-07-05T10:54:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DHuXOSq4QTcwhcqCLC1YFiaQ4iQScKEIwwgzNIoj5rDWwFNXm5XEF7drvpjqUw6/NwsfKw+ejkR5/RSKPoxVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:20:31.854337Z"},"content_sha256":"f89fe2b61191861db23b8d0b73398b033379111b2a32e1e01bff7ed1a80c96ae","schema_version":"1.0","event_id":"sha256:f89fe2b61191861db23b8d0b73398b033379111b2a32e1e01bff7ed1a80c96ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHIR543HEKYTRFRDR54ZGGW7V5/bundle.json","state_url":"https://pith.science/pith/FHIR543HEKYTRFRDR54ZGGW7V5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHIR543HEKYTRFRDR54ZGGW7V5/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":"2026-08-13T12:20:31Z","links":{"resolver":"https://pith.science/pith/FHIR543HEKYTRFRDR54ZGGW7V5","bundle":"https://pith.science/pith/FHIR543HEKYTRFRDR54ZGGW7V5/bundle.json","state":"https://pith.science/pith/FHIR543HEKYTRFRDR54ZGGW7V5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHIR543HEKYTRFRDR54ZGGW7V5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FHIR543HEKYTRFRDR54ZGGW7V5","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":"fa33ddd264fdcfd6e3036342b92bd428ebab54477280045382f051dad02bc58f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-13T03:48:15Z","title_canon_sha256":"0b507476f8800861e3d77125c51307e28efdaac759a7aa1def14f6b3c2a2d965"},"schema_version":"1.0","source":{"id":"2408.06611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.06611","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2408.06611v2","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.06611","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"FHIR543HEKYT","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"FHIR543HEKYTRFRD","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"FHIR543H","created_at":"2026-07-05T10:54:35Z"}],"graph_snapshots":[{"event_id":"sha256:f89fe2b61191861db23b8d0b73398b033379111b2a32e1e01bff7ed1a80c96ae","target":"graph","created_at":"2026-07-05T10:54:35Z","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/2408.06611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of $G_{k,n}$. This includes novel limit theorems for fixed points, cycles of various lengths, number of cycles and inversions. The limits are compound Poisson distributions with interesting dependence structure.","authors_text":"Nathan Tung, Persi Diaconis","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-13T03:48:15Z","title":"Poisson approximation for large permutation groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06611","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:ff5779ae7417b450550539cf3215fdd6184e2b67af0761f2fd962f5051218f93","target":"record","created_at":"2026-07-05T10:54:35Z","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":"fa33ddd264fdcfd6e3036342b92bd428ebab54477280045382f051dad02bc58f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-08-13T03:48:15Z","title_canon_sha256":"0b507476f8800861e3d77125c51307e28efdaac759a7aa1def14f6b3c2a2d965"},"schema_version":"1.0","source":{"id":"2408.06611","kind":"arxiv","version":2}},"canonical_sha256":"29d11ef36722b13896238f79931adfaf4f69f8fa565724bf9f45263b68ae3918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29d11ef36722b13896238f79931adfaf4f69f8fa565724bf9f45263b68ae3918","first_computed_at":"2026-07-05T10:54:35.398140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:54:35.398140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"saxzfz7va/CcOdjIn9barxhCDUEjIdv2S7BZuktdrnHqPHLwZ1fC5fbt8jJ801+lioaLhzduIKwnX6Pfv+RECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:54:35.398675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.06611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff5779ae7417b450550539cf3215fdd6184e2b67af0761f2fd962f5051218f93","sha256:f89fe2b61191861db23b8d0b73398b033379111b2a32e1e01bff7ed1a80c96ae"],"state_sha256":"7b273fb475fa6078e1fb986193cd9ae161db326bc0eeefedf8e2925d3c84f18e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVMH8IV9BODSbLjozjCdxbv7SJvxb18Xn9ev5jm3R0CIbd69EgZSfLu2wpOGpZO2aLm3b88sM8dwzKOzb9ocDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:20:31.860866Z","bundle_sha256":"ded3f139ca3f7d63622ebb6b46ee2b7604edeb398400a4cdd5a8db9b93a6e698"}}