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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16089 |
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| _version_ | 1866917416091516928 |
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| author | Combe, N. C. Nencka, H. K. |
| author_facet | Combe, N. C. Nencka, H. K. |
| contents | We present a geometric framework for reconstruction problems based on Vaisman foliations and Atiyah--Molino sequences. Independent projections induce transverse foliations and dual connections; vanishing torsion and curvature duality guarantee unique, path-independent reconstruction, while obstructions yield non-associative quasigroupoids. Toric symmetry provides equivariant uniqueness. Applications to generative AI imputation and cryo-electron microscopy demonstrate the framework's practical power, unifying differential geometry with data-driven inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16089 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Foliated Geometry of Inverse Problems: Torsion, Curvature Duality, and Near-Associativity Combe, N. C. Nencka, H. K. Differential Geometry We present a geometric framework for reconstruction problems based on Vaisman foliations and Atiyah--Molino sequences. Independent projections induce transverse foliations and dual connections; vanishing torsion and curvature duality guarantee unique, path-independent reconstruction, while obstructions yield non-associative quasigroupoids. Toric symmetry provides equivariant uniqueness. Applications to generative AI imputation and cryo-electron microscopy demonstrate the framework's practical power, unifying differential geometry with data-driven inverse problems. |
| title | Foliated Geometry of Inverse Problems: Torsion, Curvature Duality, and Near-Associativity |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.16089 |