{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LBNBYK5A7WR5ZNAHHSAAH5L4ZQ","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":"53b72a1bae7e282905ec4a14d846560c056666e7905337993cc67add02bf2780","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-03-29T19:59:00Z","title_canon_sha256":"f30b70e24df838ee35f5926804f9ccc7194d26fe7496bb2f99f324b22b9a6b8b"},"schema_version":"1.0","source":{"id":"2603.27843","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.27843","created_at":"2026-06-11T01:09:33Z"},{"alias_kind":"arxiv_version","alias_value":"2603.27843v2","created_at":"2026-06-11T01:09:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27843","created_at":"2026-06-11T01:09:33Z"},{"alias_kind":"pith_short_12","alias_value":"LBNBYK5A7WR5","created_at":"2026-06-11T01:09:33Z"},{"alias_kind":"pith_short_16","alias_value":"LBNBYK5A7WR5ZNAH","created_at":"2026-06-11T01:09:33Z"},{"alias_kind":"pith_short_8","alias_value":"LBNBYK5A","created_at":"2026-06-11T01:09:33Z"}],"graph_snapshots":[{"event_id":"sha256:682fa1b243bab682cba1d1172b0fe9b36eecb9bff2f9f0ba33a5823ef7611409","target":"graph","created_at":"2026-06-11T01:09:33Z","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/2603.27843/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The empirical Bayes $g$-modeling approach based on the nonparametric maximum likelihood estimator (NPMLE) has been central to large-scale estimation and inference in the normal means problem. However, theoretical guarantees for uncertainty quantification remain scarce. A key obstacle is that the NPMLE is necessarily discrete, which yields discrete posterior credible sets and a slow logarithmic deconvolution rate. We address both limitations by introducing a hierarchical Gaussian smoothing layer that restricts the mixing distribution to a Gaussian location mixture. Our smooth NPMLE inherits the","authors_text":"Bodhisattva Sen, Taehyun Kim","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-03-29T19:59:00Z","title":"Empirical Bayes Estimation and Inference via Smooth Nonparametric Maximum Likelihood"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27843","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:d9551f9b11e2561ffa24bbb532bacb98f6510b46882810701a73063060d298cc","target":"record","created_at":"2026-06-11T01:09:33Z","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":"53b72a1bae7e282905ec4a14d846560c056666e7905337993cc67add02bf2780","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-03-29T19:59:00Z","title_canon_sha256":"f30b70e24df838ee35f5926804f9ccc7194d26fe7496bb2f99f324b22b9a6b8b"},"schema_version":"1.0","source":{"id":"2603.27843","kind":"arxiv","version":2}},"canonical_sha256":"585a1c2ba0fda3dcb4073c8003f57ccc2c01227ebdbd20bc8b0b322eb2a6eba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"585a1c2ba0fda3dcb4073c8003f57ccc2c01227ebdbd20bc8b0b322eb2a6eba4","first_computed_at":"2026-06-11T01:09:33.935465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:33.935465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JpkIWJR8zCthyScTqKs0c9Km27ET7cCp2y/i+X0NCBJPYuNyUvQWJp80BjkkIcwM7qwqPfQv7fN//jeV4x3PBg==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:33.936421Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.27843","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9551f9b11e2561ffa24bbb532bacb98f6510b46882810701a73063060d298cc","sha256:682fa1b243bab682cba1d1172b0fe9b36eecb9bff2f9f0ba33a5823ef7611409"],"state_sha256":"e657a3a0a62e40c6dad11d3205f74a02c1d54020966a1eecc2d9ab538a34a7e8"}