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We present a general conjecture for evaluating the multiple-discontinuity integrals that appear in real-time holography using gravitational Schwinger-Keldysh (grSK) geometry. Our conjecture is valid for arbitrary non-derivative interactions with any number of bulk tree-level exchanges. It is also consistent with a unitary exterior EFT at finite temperature with correct causal structure. We present a set of Feynman rules underlying this exterior EFT and illustrate it with the computation of four and five-point functions.

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