{"paper":{"title":"Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Gromov-Hausdorff limit of orthonormal frame bundles over non-collapsed manifolds with bounded Ricci curvature has a singular set of codimension at least 4.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cuifang Si, Shicheng Xu","submitted_at":"2026-04-29T08:08:34Z","abstract_excerpt":"Let $M_i$ be a sequence of non-collapsed $n$-manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Haudorff limit space, $Y$, of the associated sequence of orthonormal frame bundles, $FM_i$, equipped with an almost canonical metric, shares similar properties as a Ricci limit space of non-collapsing sequence i.e., the singular set has codimension $\\ge 4$ whose complement contains an open and dense $C^{1,\\alpha}$-Riemannian manifold."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the singular set has codimension ≥4 whose complement contains an open and dense C^{1,α}-Riemannian manifold","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The sequence consists of non-collapsed n-manifolds with two-sided bounds on Ricci curvature, and the frame bundles are equipped with an 'almost canonical metric' whose precise definition and properties are required for the limit to behave like a Ricci limit space.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Gromov-Hausdorff limits of frame bundles of non-collapsed manifolds with two-sided bounded Ricci curvature have singular sets of codimension ≥4 whose complement is an open dense C^{1,α} Riemannian manifold.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Gromov-Hausdorff limit of orthonormal frame bundles over non-collapsed manifolds with bounded Ricci curvature has a singular set of codimension at least 4.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d75bfe0842c5a3b25ad6c7b3021c98e54659b36a1449f1bea6433319c9f1c2e1"},"source":{"id":"2604.26399","kind":"arxiv","version":2},"verdict":{"id":"9e983254-fa91-49c5-b58a-d29bc50c2d46","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:42:57.903357Z","strongest_claim":"the singular set has codimension ≥4 whose complement contains an open and dense C^{1,α}-Riemannian manifold","one_line_summary":"Gromov-Hausdorff limits of frame bundles of non-collapsed manifolds with two-sided bounded Ricci curvature have singular sets of codimension ≥4 whose complement is an open dense C^{1,α} Riemannian manifold.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The sequence consists of non-collapsed n-manifolds with two-sided bounds on Ricci curvature, and the frame bundles are equipped with an 'almost canonical metric' whose precise definition and properties are required for the limit to behave like a Ricci limit space.","pith_extraction_headline":"The Gromov-Hausdorff limit of orthonormal frame bundles over non-collapsed manifolds with bounded Ricci curvature has a singular set of codimension at least 4."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26399/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T00:37:26.301446Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:11:48.644869Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bec8e2a3bbb8933cde805d0ec2caf7cae872047ac348103766847af92c17e56c"},"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"}