H₀ as a Comparability and Global-Closure Stress Test: A Regime-Based Diagnostic

This technical note addresses the so-called H₀ tension by reframing it as a diagnostic stress test of comparability and global closure across distinct inferential regimes, rather than as a discrepancy to be resolved through new physics. We show that determinations of the Hubble constant derived from late-Universe distance ladders and early-Universe inferences based on CMB data correspond to non-isomorphic operational objects, produced by fundamentally different pipelines. Identifying these quantities as a single global parameter implicitly assumes the existence of a valid global closure bridging the two regimes. Within a regime-based diagnostic framework, the H₀ tension is therefore classified as a conditional structural tension, arising from either:(i) non-comparability between operationally distinct parameters, or(ii) failure of guaranteed global closure at the level of inference, rather than from shortcomings of the underlying physical theories. No alternative cosmological models, new entities, or extensions of standard physics are introduced. The note is methodological and diagnostic in scope, aiming to clarify the structural origin of the tension and to delineate where legitimate investigative efforts can proceed without ontological escalation.