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Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic class hierarchies currently results in puzzling type errors in most of these languages. Yet this combination of features occurs naturally in many scenarios, such as when manipulating typed ASTs. To support it properly, compilers need to implement a form of subtyping reconstruction: the ability to reconstruct subtyping information uncovered at runtime during pattern matching. We introduce cDOT, a new calculus in the family of Dependent Object Types (DOT) intended to serve as a formal foundation for subtyping reconstruction. Being descended from pDOT, itself a formal foundation for Scala, cDOT can be used to encode advanced object-oriented features such as generic inheritance, type constructor variance, F-bounded polymorphism, and first-class recursive modules. We demonstrate that subtyping reconstruction subsumes GADTs by encoding $\lambda_{2,G\mu}$, a classical constraint-based GADT calculus, into cDOT., Comment: 46 pages, 11 figures. For the associated mechanized proof of soundness, see https://zenodo.org/record/7079463. This is an extended version of the paper published at OOPSLA'22. v2 fixes typos in Fig. 3, and slightly tweaks some sentences to mirror the formally published version