Latent Capacity Under Load: Cross-Domain Application of Topological Degradation Metrics to Electrochemical and Archaeological Networks

Topological data analysis offers formal tools for measuring structural degradation in directed networks, but validation on real data remains sparse. This paper provides the first empirical test of the Latent Capacity Topology (LCT) framework on electrochemical degradation data from six lithium-ion battery cells (CALCE CS2 dataset, University of Maryland), and applies the identical pipeline to a second, materially unrelated substrate: archaeological settlement networks in the Yucatan Peninsula reconstructed from published surveys and SRTM terrain data. The primary contribution is confirmatory: total H0 persistence, computed from a sublevel Rips complex on k-distance-filtered voltage-capacity networks, declines monotonically across the degradation trajectory in all six cells. The Latent Yield (LY) metric, calibrated against a degree-preserving null model using directed edge swaps, shows statistically significant negative correlation with cycle number in two of six cells (Spearman rho < -0.9, p < 0.001) and consistent negative trend in the remaining four. The secondary contribution is exploratory: the same pipeline, applied without structural modification to a 21-site Maya settlement network around Mayapan, produces LY = 1025 at peak occupation, declining to LY = 455 after the fifteenth-century collapse. The claim advanced here is methodological generality, not substrate invariance; the aim is not to show that a single topological law governs both systems, but that one apparatus applies coherently to substrates chosen for their material distance and returns, in each, a reading that matches what is independently known about that substrate. Whether the same invariants behave identically across domains, after construction-method confounds are controlled through synthetic calibration, is a separate and harder question that this paper poses but does not answer. All code and data access instructions are provided for reproducibility.