{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YTOSMN63WO4BR6O5GU4ZWKI6RB","short_pith_number":"pith:YTOSMN63","canonical_record":{"source":{"id":"1803.04485","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2018-03-12T19:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"ba29cfd6cb36d171fc2e7bbaaf13ee598068d4acc6f54238f1944b575567728a","abstract_canon_sha256":"79109fe0d3c5b3a9f65a928ce64a7c6055a1d1b13158905788d26e538b16189c"},"schema_version":"1.0"},"canonical_sha256":"c4dd2637dbb3b818f9dd35399b291e885318ac7e204facf9a8d8c489b7f3bc80","source":{"kind":"arxiv","id":"1803.04485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04485","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04485v1","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04485","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"YTOSMN63WO4B","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YTOSMN63WO4BR6O5","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YTOSMN63","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YTOSMN63WO4BR6O5GU4ZWKI6RB","target":"record","payload":{"canonical_record":{"source":{"id":"1803.04485","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2018-03-12T19:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"ba29cfd6cb36d171fc2e7bbaaf13ee598068d4acc6f54238f1944b575567728a","abstract_canon_sha256":"79109fe0d3c5b3a9f65a928ce64a7c6055a1d1b13158905788d26e538b16189c"},"schema_version":"1.0"},"canonical_sha256":"c4dd2637dbb3b818f9dd35399b291e885318ac7e204facf9a8d8c489b7f3bc80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:18.914980Z","signature_b64":"nQd4mHZP2HYHnkC1iLEpHMFiApvfwDNqplclNmusoee4LyXas/zMWV2DtxKM7V23HMGgQmGEkQh9MRq/MZi2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4dd2637dbb3b818f9dd35399b291e885318ac7e204facf9a8d8c489b7f3bc80","last_reissued_at":"2026-05-18T00:21:18.914445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:18.914445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.04485","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":"2026-05-18T00:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enAd1poy7H564UXvPHYIJPlyC+z8syG8P2fmBuGO5c367E29WDN7ut4xTEXtGrF3DNKUlKu5U6jFAbhrih8zDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:46:00.248895Z"},"content_sha256":"d7a62b175757fa638cef23cfe27ae587aaca889c90bfa2d7ac7ad36d7b330fa6","schema_version":"1.0","event_id":"sha256:d7a62b175757fa638cef23cfe27ae587aaca889c90bfa2d7ac7ad36d7b330fa6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YTOSMN63WO4BR6O5GU4ZWKI6RB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Marianthi Markatou, Mojgan Golzy","submitted_at":"2018-03-12T19:39:37Z","abstract_excerpt":"Many applications of interest involve data that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include text mining, in particular clustering of documents, biology, astronomy and medicine among others. Previous work has proposed a clustering method using mixtures of Poisson kernel-based distributions (PKBD) on the sphere. We prove identifiability of mixtures of the aforementioned model, convergence of the associated EM-type algorithm and study its operational characteristics. Furthermore, we propose an empirical densities distance plot for estimating the number of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04485","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":"2026-05-18T00:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5UkKxdKmQT2mFQRoD4qbHQQ11Gl/DRjjq6kNqN+Ao47lxpDAC3XripOQDxYk5eLYTSdg8Ik0veBorH30UB0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:46:00.249249Z"},"content_sha256":"8ac02c7b3448d01856542728cde78e6452a2d64558a06a2f772f9d7c2d37510d","schema_version":"1.0","event_id":"sha256:8ac02c7b3448d01856542728cde78e6452a2d64558a06a2f772f9d7c2d37510d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/bundle.json","state_url":"https://pith.science/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/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":"2026-06-26T12:46:00Z","links":{"resolver":"https://pith.science/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB","bundle":"https://pith.science/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/bundle.json","state":"https://pith.science/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTOSMN63WO4BR6O5GU4ZWKI6RB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YTOSMN63WO4BR6O5GU4ZWKI6RB","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":"79109fe0d3c5b3a9f65a928ce64a7c6055a1d1b13158905788d26e538b16189c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2018-03-12T19:39:37Z","title_canon_sha256":"ba29cfd6cb36d171fc2e7bbaaf13ee598068d4acc6f54238f1944b575567728a"},"schema_version":"1.0","source":{"id":"1803.04485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04485","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04485v1","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04485","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"YTOSMN63WO4B","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YTOSMN63WO4BR6O5","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YTOSMN63","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:8ac02c7b3448d01856542728cde78e6452a2d64558a06a2f772f9d7c2d37510d","target":"graph","created_at":"2026-05-18T00:21:18Z","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":"Many applications of interest involve data that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include text mining, in particular clustering of documents, biology, astronomy and medicine among others. Previous work has proposed a clustering method using mixtures of Poisson kernel-based distributions (PKBD) on the sphere. We prove identifiability of mixtures of the aforementioned model, convergence of the associated EM-type algorithm and study its operational characteristics. Furthermore, we propose an empirical densities distance plot for estimating the number of ","authors_text":"Marianthi Markatou, Mojgan Golzy","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2018-03-12T19:39:37Z","title":"Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04485","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:d7a62b175757fa638cef23cfe27ae587aaca889c90bfa2d7ac7ad36d7b330fa6","target":"record","created_at":"2026-05-18T00:21:18Z","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":"79109fe0d3c5b3a9f65a928ce64a7c6055a1d1b13158905788d26e538b16189c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2018-03-12T19:39:37Z","title_canon_sha256":"ba29cfd6cb36d171fc2e7bbaaf13ee598068d4acc6f54238f1944b575567728a"},"schema_version":"1.0","source":{"id":"1803.04485","kind":"arxiv","version":1}},"canonical_sha256":"c4dd2637dbb3b818f9dd35399b291e885318ac7e204facf9a8d8c489b7f3bc80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4dd2637dbb3b818f9dd35399b291e885318ac7e204facf9a8d8c489b7f3bc80","first_computed_at":"2026-05-18T00:21:18.914445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:18.914445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nQd4mHZP2HYHnkC1iLEpHMFiApvfwDNqplclNmusoee4LyXas/zMWV2DtxKM7V23HMGgQmGEkQh9MRq/MZi2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:18.914980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7a62b175757fa638cef23cfe27ae587aaca889c90bfa2d7ac7ad36d7b330fa6","sha256:8ac02c7b3448d01856542728cde78e6452a2d64558a06a2f772f9d7c2d37510d"],"state_sha256":"8155ae6f27c9374ea3821064663a965114399aebe06aaf522cc3097b7091cb14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HgelymbQrR1CxRvqNAKYJ81zlspwRU/9t2DndIa+hgR8CP1eABgDCX56N0LWL0gRkKR+sI9YTUPpLg/CokFtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:46:00.254083Z","bundle_sha256":"6cb56cbbb23101e09081f5c71eb9fe891bc81cd65aeede1047b3ac7f06b1c97b"}}