{"paper":{"title":"Differentiable structures on a union of two open sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.AT","math.CT"],"primary_cat":"math.DG","authors_text":"Mykola Lysynskyi, Sergiy Maksymenko","submitted_at":"2025-07-07T16:12:18Z","abstract_excerpt":"In a recent paper the authors classified differentiable structures on the non-Hausdorff one-dimensional manifold $\\mathbb{L}$ called the line with two origins which is obtained by gluing two copies of the real line $\\mathbb{R}$ via the identity homeomorphism of $\\mathbb{R}\\setminus 0$.\n  Here we give a classification of differentiable structures on another non-Hausdorff one-dimensional manifold $\\mathbb{Y}$ (called letter \"$Y$\") obtained by gluing two copies of $\\mathbb{R}$ via the identity map of positive reals. It turns out that, in contrast to the real line, for every $r=1,\\ldots,\\infty$, b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05156","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/2507.05156/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"}