A.1 Experimental design Figure 1 summarizes the experimental design used for our experiments. The participants that went through our experiments are users from the online platform Amazon Mechanical Turk (AMT). Through this platform, users stay anonymous, hence, we do not collect any sensitive personal information about them. We prioritized users with a Master qualification (which is a qualification attributed by AMT to users who have proven to be of excellent quality) or normal users with high qualifications (number of HIT completed = 10000and HIT accepted > 98%). Before going through the experiment, participants are asked to read and agree to a consent form, which specifies: the objective and procedure of the experiment, as well as the time expected to completion ( 5 - 8 min) with the reward associated ($1.4), and finally, the risk, benefits, and confidentiality of taking part in this study.

Spiking reservoir computing provides an energy-efficient approach to temporal processing, but reliably tuning reservoirs to operate at the edge-of-chaos is challenging due to experimental uncertainty. This work bridges abstract notions of criticality and practical stability by introducing and exploiting the robustness interval, an operational measure of the hyperparameter range over which a reservoir maintains performance above task-dependent thresholds. Through systematic evaluations of Leaky Integrate-and-Fire (LIF) architectures on both static (MNIST) and temporal (synthetic Ball Trajectories) tasks, we identify consistent monotonic trends in the robustness interval across a broad spectrum of network configurations: the robustness-interval width decreases with presynaptic connection density $β$ (i.e., directly with sparsity) and directly with the firing threshold $θ$. We further identify specific $(β, θ)$ pairs that preserve the analytical mean-field critical point $w_{\text{crit}}$, revealing iso-performance manifolds in the hyperparameter space. Control experiments on Erdős-Rényi graphs show the phenomena persist beyond small-world topologies. Finally, our results show that $w_{\text{crit}}$ consistently falls within empirical high-performance regions, validating $w_{\text{crit}}$ as a robust starting coordinate for parameter search and fine-tuning. To ensure reproducibility, the full Python code is publicly available.

Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely separation, robustness, and fading memory) still lack rigorous mathematical foundations. This paper addresses this gap by providing a control-theoretic framework for the analysis of time-delay-based reservoir computers. We introduce formal definitions of the separation property and fading memory in terms of functional norms, and establish their connection to well-known stability notions for time-delay systems as incremental input-to-state stability. For a class of linear reservoirs, we derive an explicit lower bound for the separation distance via Fourier analysis, offering a computable criterion for reservoir design. Numerical results on the NARMA10 benchmark and continuous-time system prediction validate the approach with a minimal digital implementation.

The civilization made the most of its technology, but everything has its limits. Mayan society often relied on cinnabar, a deep red pigment that got its hue from mercury sulfide. Breakthroughs, discoveries, and DIY tips sent six days a week. A trio of ancient reservoirs in present-day Guatemala is revealing both the strength--and limitations--of Mayan water science. While the civilization's purification techniques resulted in comparatively clean drinking sources, archaeologists say the unknowable consequences of a commonly used, deep-red pigment consistently subjected the Indigenous population to toxic mercury poisoning .