Tolerance-Limited Spacing in Multi-Vortex Configurations: A Stability Corridor Analysis

Structure, stability, and emergence are governed not by absolute resolution, but by the ratio between the resolution of the underlying relational system and the resolution of the projection used to observe it. This work investigates the emergence and spacing of stable multi-structure configurations in driven systems through the lens of a finite relational tolerance interval. Using galactic rotation curve data (radial acceleration relation) and solar X-ray observations, we identify a narrow stability corridor in which configuration variance is strongly suppressed and multiple structures coexist without merging or fragmenting. The width of this corridor, defined as the difference between empirically observed coherence thresholds, matches the characteristic spacing between stable configurations to within measurement uncertainty. We show that coupling strength peaks near the boundaries of this tolerance interval, consistent with intensified merge and fragment dynamics at stability limits. These results support a constraint-driven mechanism in which structure arises not from stochastic forcing or energy optimization, but from the impossibility of perfect coordination beyond a finite adjustment range. We further argue that the relevant observables are ratio-type parameters requiring harmonic statistical treatment, which improves agreement between observed spacings and predicted tolerance scales. The framework is falsifiable and domain-agnostic: it predicts where stable configurations can exist, when defects or curvature must appear, and how harmonic and resonant structures are constrained by tolerance limits. If confirmed in additional systems, tolerance-limited spacing offers a general principle for understanding scale selection and structure formation across physical and complex systems.