{"paper":{"title":"Diffeological Riemannian orbifolds","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Miyamoto","submitted_at":"2026-07-09T21:08:20Z","abstract_excerpt":"We show that the data of a Riemannian metric on a differentiable stack presented by an orbifold groupoid is equivalent to the data of a Riemannian metric on its diffeological orbit space. As a consequence, we conclude that the classical notion of Riemannian orbifold is equivalent to that of a Riemannian diffeological orbifold. We use the framework for Riemannian diffeology introduced by Kuribayashi, Sakai, and Shiobara, and our result answers a problem they posed in the affirmative. More generally, we show that a Riemannian metric on a Lie groupoid, namely a 2-metric in the sense of del Hoyo a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08939","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/2607.08939/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"}