{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NKFTUUNAJMEOFGKDYM52JQ7D5J","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":"6a149789e20da921d22858929cecd4f716ae5c6ef155ea128f8527f396b0753c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-08-23T15:09:50Z","title_canon_sha256":"709e88df37ed32dc3774934d8516286feb46637d9fc0587c84399e3f85705f32"},"schema_version":"1.0","source":{"id":"1608.06536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06536","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06536v1","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06536","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"NKFTUUNAJMEO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NKFTUUNAJMEOFGKD","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NKFTUUNA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:fc3302849e2c9149d264b0a606e6ff7c0db475326d810c83d16c6dda9827d4c6","target":"graph","created_at":"2026-05-18T01:08:13Z","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":"Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not proved, that the situation should be reversed under heavy tails assumptions. The conjecture is based on the feeling that there is no need to achieve a good order of approximation in regions with few data (say, in the tails), favoring location-scale mixtures which allow for spatially varying order of approximation. Here we test the previous argument on the Gaus","authors_text":"Judith Rousseau, Zacharie Naulet","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-08-23T15:09:50Z","title":"Tails assumptions and posterior concentration rates for mixtures of Gaussians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06536","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:b7ac45cf906343a824f4d1336e2dd2ff3a32a61af8b3757930a1b78b13f71a11","target":"record","created_at":"2026-05-18T01:08:13Z","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":"6a149789e20da921d22858929cecd4f716ae5c6ef155ea128f8527f396b0753c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-08-23T15:09:50Z","title_canon_sha256":"709e88df37ed32dc3774934d8516286feb46637d9fc0587c84399e3f85705f32"},"schema_version":"1.0","source":{"id":"1608.06536","kind":"arxiv","version":1}},"canonical_sha256":"6a8b3a51a04b08e29943c33ba4c3e3ea79d171c83a1a26c4ffba7a0e43a8018d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a8b3a51a04b08e29943c33ba4c3e3ea79d171c83a1a26c4ffba7a0e43a8018d","first_computed_at":"2026-05-18T01:08:13.825938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:13.825938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JqKzIcIYiA3/2yQElTR8uanrQIuS9ItiFbeqLIS0bNVn5ajxdOF1evNqCHrumiK3/U6QCaABW+EmOAXnaoIHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:13.826582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7ac45cf906343a824f4d1336e2dd2ff3a32a61af8b3757930a1b78b13f71a11","sha256:fc3302849e2c9149d264b0a606e6ff7c0db475326d810c83d16c6dda9827d4c6"],"state_sha256":"9bf0e0966e8d39e2d05eecd4a4a446058b59529c05dfd3eba765819c202270b0"}