The Quantum Spectral Curve (QSC) has proven to be a powerful framework for computing the spectrum of integrable quantum field theories, particularly in the context of N=4 supersymmetric Yang–Mills theory. In this project, we aim to extend the applicability of the QSC beyond its standard domain, exploring new theories and spectral trajectories—going beyond the leading Regge trajectory. Additionally, we pursue the construction of numerical QSC transfer matrices, which serve as essential building blocks in a recently proposed approach for computing structure constants. Our goal is to leverage these tools to gain deeper insights into the dynamics of integrable models and to further develop the QSC as a versatile computational method in quantum field theory.1