Operational Cost and Structural Stabilization in Computation: A Balance-Preserving Framework f

We propose a general framework for analyzing computational processes in terms of an opera- tional stabilization cost, K, which quantifies the structural effort required to maintain coherence of intermediate states during computation. Unlike classical complexity measures, K captures a complementary, pre-computational aspect: the cost of organizing relational structures underly- ing algorithms, solvers, and learning systems. K is defined on a relational graph representation as a gauge-invariant sum of cycle-induced frustration and spectral rigidity terms.1 While not altering algorithmic complexity classes, K provides a principled diagnostic for early stopping, structural pruning, and convergence as- sessment. We present minimal examples, reproducible case studies, falsifiable predictions with quantitative benchmarks, and an explicit discussion of limitations. Code and experimental pro- tocols are provided to ensure reproducibility. We additionally provide a five-loop validation protocol (Loop-5) that operationalizes internal consistency checks, limiting-case reductions, fal- sifiable constraints, implementability gates, and external interpretability.