Beyond the question of deuterium's mean value lies the question of its map. If Big Bang nucleosynthesis happened once, identically everywhere, then the primordial D/H ratio is a universal constant, and measurements along different sightlines, toward different quasars, through absorbers at different redshifts and sky positions, must agree up to measurement error and the slow one-way destruction of deuterium in stars.
The map shows texture the uniformity forbids. The measured ensemble exhibits statistical dispersion beyond formal uncertainties, and analyses have flagged potential structure with redshift and direction, not yet decisive, but persistent across measurement generations (Cooke et al. 2014 for the precision benchmark; the wider literature for the dispersion). For ΛCDM the stakes escalate with each possibility: scatter from systematics is benign, scatter from varied astration is manageable but requires star-formation histories more diverse than smooth assembly provides, and genuine spatial variation of the primordial ratio would be fatal, since the model's single global BBN event has no mechanism for making different deuterium in different places.
The standing is data-limited in a specific way: the clean-absorber sample is small, each measurement is hard-won, and distinguishing dispersion's causes requires the per-absorber metallicity and environment information that only the next spectroscopic generation will supply in bulk.