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Recent AI models show promise in vericoding, but a unified methodology for cross-paradigm evaluation is lacking. Existing benchmarks test only individual languages/tools (e.g., Dafny, Verus, and Lean) and each covers very different tasks, so the performance numbers are not directly comparable. We address this gap with AlgoVeri, a benchmark that evaluates vericoding of $77$ classical algorithms in Dafny, Verus, and Lean. By enforcing identical functional contracts, AlgoVeri reveals critical capability gaps in verification systems. While frontier models achieve tractable success in Dafny ($40.3$% for Gemini-3 Flash), where high-level abstractions and SMT automation simplify the workflow, performance collapses under the systems-level memory constraints of Verus ($24.7$%) and the explicit proof construction required by Lean (7.8%). 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