{"paper":{"title":"Extreme Points of the $(0,\\delta)$-LDP Polytope with Small Input Size and Arbitrary Output Sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anand Sarwate, Gowtham R. Kurri, Myna Vajha, Supriya Rawat","submitted_at":"2026-06-08T07:53:59Z","abstract_excerpt":"The structure of locally differentially private (LDP) mechanisms can be understood through the geometry of the corresponding privacy polytope. While the extreme points of the \\( (\\epsilon,0)\\)-LDP polytope are well characterized (Kairouz \\emph{et al.}, 2014; Holohan \\emph{et al.}, 2017; Pensia \\emph{et al.}, 2017), comparatively little is known for the \\((\\epsilon,\\delta)\\)-LDP polytope with \\(\\delta>0\\). Recent work (Elangovan and Jog, 2024) has shown that even in the special case \\(\\epsilon=0\\), the \\( (0,\\delta) \\)-LDP privacy polytope exhibits fundamentally different behaviour. In this wor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09161","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/2606.09161/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"}