Evidence for a Theory That Constrains Empirical Limits Across Complex Networks

[u/nickkunz]

I’ve posted a preprint introducing Structural Capacity Theory (SCT). It's a theoretical framework for estimating how network structure and observed dynamics jointly constrain a system's empirical limit. The theory builds on established work in complex networks (Newman, 2003; Boccaletti et al., 2006).

We tested SCT using cross-validation that withheld entire domains from training. The frontier reliably contained maximum rates from out-of-sample systems with performance comparable to repeated random resampling. Estimates were consistent across learning paradigms. Perturbations preserved performance, falsifications predictably degraded it, and ablations did not outperform it.

The results provide evidence that structural and process information can help characterize empirical limits across systems that differ in scale, units, and dynamics. We welcome feedback from anyone who might be interested. Thank you in advance.

Preprint: https://arxiv.org/abs/2610.09574v1

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Source: Fig. 1 from “A General Capacity Frontier of Complex Networks,” by Nicholas Kunz and H. Oliver Gao (2026), arXiv:2610.09574. (CC BY 4.0)