{"paper":{"title":"A Fast Gaussian Mechanism under Continual Observation, with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DB"],"primary_cat":"cs.DS","authors_text":"Rasmus Pagh, Sia Sejer","submitted_at":"2026-06-10T07:36:58Z","abstract_excerpt":"We consider the problem of privately releasing a $k$-dimensional vector under updates: Starting with a zero vector, at times $t_1, t_2,\\dots$ the vector is updated by adding $x^{(1)}, x^{(2)},\\dots$, respectively. For positive integers $T$, $k$ we model the updates as a data set $\\{(t_i, x^{(i)})\\}_i$, where $t_i \\in [T]$ and $x^{(i)} \\in B_k$ (the $k$-dimensional unit ball). Two such data sets are said to be neighboring if their symmetric difference has size at most $1$. The continual release consists of the sum $A^{(t)} = \\sum_{i \\; : \\; t_i \\leq t} x^{(i)}$ for each time step $t=1,\\dots,T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11760","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11760/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}