{"paper":{"title":"Closed $4$--Manifolds Foliated by Hyperplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Harold Rosenberg, Jos\\'e M. Espinar","submitted_at":"2026-06-06T06:46:33Z","abstract_excerpt":"Let $M^4$ be a closed, orientable $4$--manifold carrying a transversely oriented $C^2$ codimension--one foliation whose leaves are diffeomorphic to $\\mathbb{R}^3$. We prove that $M^4$ is homeomorphic to the $4$--torus $\\mathbb{T}^4$. We also show that, whenever the original smooth structure on $M$ admits a smooth defining $1$--form, the conclusion sharpens to a diffeomorphism $M\\cong\\mathbb{T}^4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08005","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/2606.08005/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"}