BAO as a Cross-Regime Comparability and Global-Closure Stress Test

This technical note examines Baryon Acoustic Oscillations (BAO) as a cross-regime inferential object, reframing their role from that of an independent “standard ruler” to that of a procedural bridge enforcing global closure between early- and late-Universe regimes. Rather than questioning the physical origin of BAO or the validity of standard cosmological models, the analysis focuses on the comparability conditions required to identify the primordial sound horizon with the BAO scale observed in large-scale structure. We show that these quantities constitute non-isomorphic operational objects, linked through model-dependent mappings that render their identification conditional rather than guaranteed. Within a regime-based diagnostic framework, BAO are therefore interpreted as a stabilizing element of global inference, whose apparent success reflects the strength of the imposed closure rather than an independent validation of it. This perspective clarifies the epistemic function of BAO in joint cosmological analyses and delineates the limits within which BAO-based comparability remains legitimate. No new physics, alternative cosmological models, or additional entities are introduced. The note is methodological and diagnostic in scope, aiming to make explicit the structural assumptions underlying BAO-mediated global closure.