{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TSDHHWZJQRU3LQNZNYJR6NROIY","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":"35a380a91eb08445f4419ca11bb9293811bfb86f1917d5cf306c1b851feaef51","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T11:43:43Z","title_canon_sha256":"c3bfce16768005508447bcd9397e1dc5c8233fe1f5a46ec0c36aff8f8c850cfb"},"schema_version":"1.0","source":{"id":"2606.13230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13230","created_at":"2026-06-12T01:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13230v1","created_at":"2026-06-12T01:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13230","created_at":"2026-06-12T01:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"TSDHHWZJQRU3","created_at":"2026-06-12T01:09:47Z"},{"alias_kind":"pith_short_16","alias_value":"TSDHHWZJQRU3LQNZ","created_at":"2026-06-12T01:09:47Z"},{"alias_kind":"pith_short_8","alias_value":"TSDHHWZJ","created_at":"2026-06-12T01:09:47Z"}],"graph_snapshots":[{"event_id":"sha256:2ce1836853cb08929e57232abf30944b570188d4e9ec600b9b51f7a8f551744c","target":"graph","created_at":"2026-06-12T01:09:47Z","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/2606.13230/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variational methods are widely used to approximate posterior distributions in Bayesian inference when exact computation is infeasible. We study when such approximations inherit posterior consistency. Our first result shows that, on a general metric space, a uniform bound on the Kullback--Leibler divergence from the approximating measures to a tight sequence of target measures forces the approximating sequence to be tight. It follows that if the target posteriors converge weakly to a Dirac mass at the true parameter, then any variational sequence with bounded Kullback--Leibler divergence to the","authors_text":"Hien Duy Nguyen, Jacob Westerhout, Julyan Arbel, Thomas Guilmeau","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T11:43:43Z","title":"Consistency of variational approximations under bounded Kullback--Leibler divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13230","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":"sha256:8f13066982d4cef495a2bd47b2c1e72a0b5233a74b62afc293c1a71189a454d0","target":"record","created_at":"2026-06-12T01:09:47Z","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":"35a380a91eb08445f4419ca11bb9293811bfb86f1917d5cf306c1b851feaef51","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T11:43:43Z","title_canon_sha256":"c3bfce16768005508447bcd9397e1dc5c8233fe1f5a46ec0c36aff8f8c850cfb"},"schema_version":"1.0","source":{"id":"2606.13230","kind":"arxiv","version":1}},"canonical_sha256":"9c8673db298469b5c1b96e131f362e4633561ecfaebf68795258bbcb7220d0b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c8673db298469b5c1b96e131f362e4633561ecfaebf68795258bbcb7220d0b0","first_computed_at":"2026-06-12T01:09:47.773675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:47.773675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQFryIBWzHmrkrTc0RfSzYtw+DMomnSLdnpggQEoLVPfhEabrgEE7ejeOpf8pIOAtqzcXJPnwFsC/1LOOqY8Bg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:47.774519Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f13066982d4cef495a2bd47b2c1e72a0b5233a74b62afc293c1a71189a454d0","sha256:2ce1836853cb08929e57232abf30944b570188d4e9ec600b9b51f7a8f551744c"],"state_sha256":"50cb844d9796dc6a11885b12a4565bb4f97878918955f58bdf677d3245056fab"}