Observer-Dependence in Empirical Inference: The Observer-Dependence Index (ODI) as a Diagnostic Framework

We introduce the Observer-Dependence Index (ODI), a quantitative diagnostic designed to measure how empirical classifications depend on the structural assumptions preserved by different null models. Rather than treating observer dependence as a binary property, the framework compares multiple null models that preserve progressively more structure (e.g., independence, short-range correlation, block coherence) and tracks how statistical significance changes across these choices. Applied to high-resolution solar X-ray time-series data, the diagnostic reveals that apparently contradictory classifications—“structural” under permutation nulls and “baseline” under autoregressive nulls—reflect genuine scale-dependent organization, not methodological failure. The ODI captures this behavior by quantifying classification stability across null models, identifying the scales at which structure is real, attenuated, or indistinguishable from baseline dynamics. The framework is theory-agnostic and portable across domains. It does not introduce new physical assumptions or fitted parameters, but formalizes best practices in null testing and robustness analysis into a single, interpretable metric. The Observer-Dependence Index provides a practical tool for resolving disagreements driven by modeling choices and for clarifying the scale at which empirical structure is meaningfully observable.