Evaluating a posteriori geometric hypotheses in spatial data: constrained logarithmic curve patterns in a summit landscape

Geometric patterns identified in spatial data after inspection are difficult to evaluate statistically. When hypotheses are formulated a posteriori, conventional tests can overestimate significance because exploratory choices are not accounted for. This problem is pronounced in small-N spatial point sets, where model flexibility and feature selection strongly influence outcomes.A constrained evaluation framework is applied to assess a posteriori geometric hypotheses in spatial data. The approach limits the geometric degrees of freedom and conditions tests on a fixed set of candidate points. It is intended for situations in which a geometric pattern is first observed and then formally assessed. Point-to-curve deviations are used to compare the observed configuration with alternative spatial and geometric arrangements subject to specified constraints.The framework is demonstrated using a summit landscape in Central Bosnia, where a constrained logarithmic curve pattern has been proposed to link a small set of named summit locations derived from LiDAR data. The observed configuration occupies an extreme position relative to alternative constrained configurations within the defined summit set.The analysis is limited to spatial geometry and does not address origin or interpretation. The contribution is a transparent method for evaluating a posteriori geometric hypotheses in small-N spatial datasets.