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The complexity of browsers has steadily increased over the years, driven by the continuous introduction and update of Web platform components, such as novel Web APIs and security mechanisms. Their specifications are manually reviewed by experts to identify potential security issues. However, this process has proved to be error-prone due to the extensiveness of modern browser specifications and the interplay between new and existing Web platform components. To tackle this problem, we developed WebSpec, the first formal security framework for the analysis of browser security mechanisms, which enables both the automatic discovery of logical flaws and the development of machine-checked security proofs. WebSpec, in particular, includes a comprehensive semantic model of the browser in the Coq proof assistant, a formalization in this model of ten Web security invariants, and a toolchain turning the Coq model and the Web invariants into SMT-lib formulas to enable model checking with the Z3 theorem prover. If a violation is found, the toolchain automatically generates executable tests corresponding to the discovered attack trace, which is validated across major browsers. We showcase the effectiveness of WebSpec by discovering two new logical flaws caused by the interaction of different browser mechanisms and by identifying three previously discovered logical flaws in the current Web platform, as well as five in old versions. Finally, we show how WebSpec can aid the verification of our proposed changes to amend the reported inconsistencies affecting the current Web platform.