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Our work advances significantly the state-of-the-art in the study of complexity, allowing the analysis of the geometric properties of many model energies that do not belong to the narrow class for which quenched averages and annealed averages are equal. This advances path-breaking work by Ros et al. in PRX 9 011003 (2019) by extending the methods they pioneered. Providing a conjecture for the quenched complexity also pushes forward the mathematics of complexity, which has been interested in these models as in Ben Arous et al., Comm. Pure Appl. Math., 72 2282.
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