{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3G55JDERLMUNWOWTOF62KWNJ52","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":"5f20f740f30f3642b13e98bec4860a4196521ff49491e21fd94e5e87d384a255","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-10-03T17:01:34Z","title_canon_sha256":"22ec8b7aa87f0bbfc4043448cfd788e3cce05e289cd09108cc6ebfad81c5f56f"},"schema_version":"1.0","source":{"id":"1310.1034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1034","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1034v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1034","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"3G55JDERLMUN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3G55JDERLMUNWOWT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3G55JDER","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:bfb67dea6a9325a3b4ab5105d8535cf477d86c26c30bdb0d00d3e2e577e1b3af","target":"graph","created_at":"2026-05-18T03:11:24Z","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":"An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise co-occurrence. The method is based on subset convolution, and yields the posterior distribution for the number of clusters in O(n * 3^n) operations, or O(n^3 * 2^n) using fast subset convolution. Pairwise co-occurrence probabilities are then obtained in O(n^3 * 2^n) operations. This is considerably faster than exhaustive enumeration of all partitions.","authors_text":"Jukka Corander, Jukka Kohonen","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-10-03T17:01:34Z","title":"Computing Exact Clustering Posteriors with Subset Convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1034","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:d83015ee39b01367a203e0dde8630d26749dcd79e577144be2eb3051cceb2739","target":"record","created_at":"2026-05-18T03:11:24Z","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":"5f20f740f30f3642b13e98bec4860a4196521ff49491e21fd94e5e87d384a255","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-10-03T17:01:34Z","title_canon_sha256":"22ec8b7aa87f0bbfc4043448cfd788e3cce05e289cd09108cc6ebfad81c5f56f"},"schema_version":"1.0","source":{"id":"1310.1034","kind":"arxiv","version":1}},"canonical_sha256":"d9bbd48c915b28db3ad3717da559a9ee8c62a58dc56ea41c6346d4baac7f166a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9bbd48c915b28db3ad3717da559a9ee8c62a58dc56ea41c6346d4baac7f166a","first_computed_at":"2026-05-18T03:11:24.689007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.689007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bYQ0Bb54lYOBoqrj+1klIbjkVD+1ky/OuWh/vlkUYvo7d7RQ2rTgBEhkUn1v6gah4lOgY6VggLnN3nHsjcs3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.689554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d83015ee39b01367a203e0dde8630d26749dcd79e577144be2eb3051cceb2739","sha256:bfb67dea6a9325a3b4ab5105d8535cf477d86c26c30bdb0d00d3e2e577e1b3af"],"state_sha256":"58e61baf3b5fa85471b985f5efa6690c9b85ab87868fc014f75285363e81f3ee"}