{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:G7DQ2PLI5DGI5FLYMTWPZCBQY6","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":"185e4fb80768e9117a6474569c4952e855b1c08da0c32f164c663e43226985be","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-24T07:19:53Z","title_canon_sha256":"252813ad5f41f52586efa9b4c60a3d5d51ff569bf527b3e8a26c786b88845c72"},"schema_version":"1.0","source":{"id":"2606.25492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25492","created_at":"2026-06-25T01:18:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25492v1","created_at":"2026-06-25T01:18:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25492","created_at":"2026-06-25T01:18:06Z"},{"alias_kind":"pith_short_12","alias_value":"G7DQ2PLI5DGI","created_at":"2026-06-25T01:18:06Z"},{"alias_kind":"pith_short_16","alias_value":"G7DQ2PLI5DGI5FLY","created_at":"2026-06-25T01:18:06Z"},{"alias_kind":"pith_short_8","alias_value":"G7DQ2PLI","created_at":"2026-06-25T01:18:06Z"}],"graph_snapshots":[{"event_id":"sha256:36bbfca8a6ed1fb949d331480ed3d059250587fe56fcfb50b791ff9d30c0dca6","target":"graph","created_at":"2026-06-25T01:18:06Z","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/2606.25492/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Donsker--Varadhan formula characterizes the ordinary Bayesian posterior as the solution of an unrestricted $\\mathsf{KL}$-regularized variational problem. Generalized variational inference replaces this regularizer by other divergences, but the resulting measure-valued optimization problem is often studied only after restriction to a parametric variational family. This paper studies the unrestricted measure-level problem. Given a measurable space $(\\mathcal{Z},\\mathfrak{Z})$, a prior probability measure $P$, a measurable loss $\\ell:\\mathcal{Z}\\to(-\\infty,\\infty]$, a regularization strength ","authors_text":"Hien Duy Nguyen, Jacob Westerhout","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-24T07:19:53Z","title":"Closed-form solutions to some generalized variational inference problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25492","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":"sha256:9b93ec8a3dbf13baf5d4349df180f07e2cdc7b4b8100e4f181659d6fe77390f0","target":"record","created_at":"2026-06-25T01:18:06Z","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":"185e4fb80768e9117a6474569c4952e855b1c08da0c32f164c663e43226985be","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-24T07:19:53Z","title_canon_sha256":"252813ad5f41f52586efa9b4c60a3d5d51ff569bf527b3e8a26c786b88845c72"},"schema_version":"1.0","source":{"id":"2606.25492","kind":"arxiv","version":1}},"canonical_sha256":"37c70d3d68e8cc8e957864ecfc8830c78111e10b578980bdb1857cf4d7ccac57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c70d3d68e8cc8e957864ecfc8830c78111e10b578980bdb1857cf4d7ccac57","first_computed_at":"2026-06-25T01:18:06.818808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:06.818808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyI5/gosFyWKm9tABLzHuJ3ILHIRUMKsukoyZBQjVHyRTct0FXKGKD+uifHxnreGdyO02VgPPAXu/VV8VZKDAQ==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:06.819249Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b93ec8a3dbf13baf5d4349df180f07e2cdc7b4b8100e4f181659d6fe77390f0","sha256:36bbfca8a6ed1fb949d331480ed3d059250587fe56fcfb50b791ff9d30c0dca6"],"state_sha256":"38e4c6525162faa11d7dea0183b5dac2bff605de8875740770fd95277eac7acf"}