Four Claims Tested on One Landscape: A Self-Falsification Study in Topological Data Analysis

This article takes four claims from the author's own prior work on topological degradation metrics, tests each against a control on a single real substrate, and reports that three of the four do not survive. The substrate is a fire-prone landscape in the Sierra de Ancares, northwestern Spain, for which a published 100-member random forest ignition ensemble and a static predictor stack are available, and for which ERA5-Land reanalysis supplies the meteorology from which two established fire indices are computed. The first claim, that one-dimensional persistent features are near the detection threshold on this landscape, was an artifact of a truncated download: the complete ensemble puts H1 prevalence at seventeen percent rather than three. The second claim, that zero-dimensional persistence declines monotonically along a spatial ignition gradient at a rank correlation of unity, is close to tautological, because the gradient variable is the node count rescaled and total persistence scales with node count; normalized, the relationship reverses. The third claim, that a negative Latent Yield indicates intrinsic sub-random structure, fails because the sign of that quantity inverts between two defensible null models, as companion work demonstrates on two independent citation benchmarks. The fourth claim, that the magnitude of a negative Latent Yield measures a property of the system, fails outright: a two-by-two control shows the negative reading persists when the attribute autocorrelation is destroyed, when the spatial embedding is destroyed, and when both are, establishing that the quantity reports the difference between a nearest-neighbour graph and its degree-preserving rewiring rather than anything about the landscape. What survives is a single result, and it survives precisely because it depends on none of the machinery that failed: on a network whose node set is held fixed at 389, total zero-dimensional persistence tracks dead fuel moisture across the fire season at a rank correlation of 0.964 with p equal to 0.00045, and is flat against ignition probability across one hundred ensemble members. This article is a companion to a methodological treatment of construction, null, and autocorrelation sensitivity, and supplies the empirical case that the treatment argues in the abstract.