The Coordination Principle - Geometric Limits to the Observer's Basis - A variational criterion for admissible degrees of freedom

Physics routinely switches descriptive bases for the same underlying system—local values, distributions, collective fields, correlators, graphs, and topology. Prior work in the “Periodic Table of Physical Descriptions” series organized these choices into a row ladder of primary objects (values → distributions → collective fields → correlations → relations → topology → phase classes) and showed empirically that higher-row observables (relations/topology) are often far more stable under representation change than lower-row observables (values/fields). Separately, the reference-frame trilogy established that physical observers cannot maintain perfect geometric simultaneity across arbitrarily large regions due to finite access, quantum diffusion, and gravitational desynchronization. This paper unifies those results into a single physical constraint on variable choice. We introduce the Coordination Principle: a degree-of-freedom (DOF) basis is admissible only if the observer can maintain the geometric coordination required to define its variables simultaneously across the region of interest. When coordination fails, descriptions based on pointwise field values become physically unstable, forcing transitions to relational and topological bases that remain meaningful under simultaneity loss. We formalize this using a variational selection rule, the Principle of Least Descriptive Instability, minimizing a descriptive actionS_D(B) = predictive error + λ × (frame-induced instability),where the instability term captures irreducible variability due to coordination limits and reconstruction ambiguity. As an empirical anchor, we analyze DES Y3 weak-lensing convergence reconstructions (KS, Wiener, NullB, GLIMPSE) under a common mask. The coefficient of variation (CV) across pipelines shows a strict stability hierarchy: Row V (value-based statistic): CV = 1.468 Row R (relational graph statistic): CV = 0.0489 Row T (topological invariant): CV = 0.0150corresponding to an ~100× stability advantage of Row T over Row V on identical data. The same qualitative ordering persists under tomographic perturbations. These results support a practical conclusion: basis selection in physics is constrained not only by dynamics and computation, but by the geometric capacity of the observer’s reference frame to coordinate measurements. The periodic taxonomy becomes a constraint map dictated by spacetime coherence, and a guide for stability-first inference in finite-access sciences such as cosmology. Keywords coordination principle; degrees of freedom; basis selection; representation stability; finite access; reference frames; simultaneity loss; weak gravitational lensing; DES Y3; mass mapping; reconstruction priors; graph invariants; persistent homology; Betti numbers; topology-first inference; stability-first inference; causal discovery; transfer entropy