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In this talk, we address a keystone problem in quantum foundations: the systematic factorisation of S-matrices. We develop an approach based on a subtle mix of geometric and Berezin-Toeplitz quantization. Within this framework, we demonstrate how the Stokes phenomenon鈥攁rising in the semiclassical analysis of Schr枚dinger equations in coherent-state representations鈥攑rovides a natural mechanism of approximate factorisation of S-matrices into discrete products. After discussing conditions for these product decompositions to be finite, we argue that this procedure offers a novel framework for quantum emulation. This is joint work with Steven Rayan, and the manuscript is currently in preparation.
