Avoiding logical strength in analysis

In reverse mathematics, one classically represents real numbers by Cauchy sequences (q_n) with a known rate of convergence, where typically |q_m-q_n|<2^{-m} for m<n. While this has good reasons, it turns out that "slow" Cauchy sequences (without prescribed rate of convergence) have great advantages as well: In joint work with Nicholas Pischke and Patrick Uftring (arXiv:2605.15151), we have shown that almost all one-dimensional real analysis from the textbook by Simpson can be developed in theories that are Pi^1_1-conservative over RCA_0 (including results that require ACA_0 with the classical representation). This yields a very different picture of the foundations of analysis, which also blurs the boundary between analytical principles and combinatorial principles from the so-called reverse mathematics zoo.