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We prove R\\'enyi QNEC for all integer R\\'enyi parameters $n\\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. 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We prove R\\'enyi QNEC for all integer R\\'enyi parameters $n\\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. Concretely, for any $\\sigma$-finite von"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove Rényi QNEC for all integer Rényi parameters n≥2 for von Neumann algebras carrying a half-sided modular inclusion structure. 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