Traditional second-order-in-time space–time discretizations of the wave equation typically require a CFL condition for stability. Recent works by O. Steinbach and M. Zank (2019), and S. Fraschini, G. Loli, A. Moiola, and G. Sangalli (2024) have introduced unconditionally stable schemes using maximal regularity splines in time, incorporating non-consistent penalty terms in the bilinear forms. While stability and error analyses have been rigorously established for low-order spaces, a full theoretical framework for higher-order methods is still lacking, despite their promising numerical performance. In M. Ferrari and S. Fraschini (2025), we address this gap by analyzing the condition number behavior of a family of matrices arising from the time discretization. For each spline order, we derive explicit estimates of both the CFL condition required for the unstabilized scheme and the optimal penalty parameter that minimizes the consistency error in the stabilized scheme. Furthermore, in M. Ferrari, S. Fraschini, G. Loli and I. Perugia (2024), we show that a first-order-in-time formulation, in contrast with second-order-in-time formulations, is unconditionally stable without the need for stabilization terms. In this talk, we focus on this mathematical technique which provides insights into the stability of families of conforming space–time discretizations for the wave equation employing maximal regularity splines in time. The idea is to address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. The system matrices result well-conditioned (in a sense that will be specified) if the associated polynomial symbols have a certain number of zeros of unitary modulus.