Beyond Coverage: Which Observations Share an Instance Decides What a Joint Model Can Learn

Joint models learn from partially observed instances; designs are compared by coverage, how often each variable and pair is observed, not which observations share an instance. If three variables vary widely but their sum barely does, observing all three measures the sum's variance; observing pairs assembles it from far larger entries. For a Gaussian joint we define a design's information operator and prove that coverage fixes its trace, leaving its spectrum to which observations share an instance. The spectrum sets sample cost: at identical coverage, an isolated direction's variance costs a fixed number of instances when some instance observes all its variables and, for any estimator, one growing as the inverse square of that variance when none does. Moment and likelihood learners can rank coverage-matched designs oppositely. On budget-matched echocardiogram acquisition policies, our operator predicts the likelihood learner's covariance estimation error within 3.2% with known truth, and a bound from a small pilot, before any fit, orders the policies, coverage-matched pairs included, as held-out likelihood does. A constructed domain realises the separation at four orders of magnitude. Coverage fixes how much a design observes; which observations share an instance decides what an unrestricted joint model can learn. Code: https://anonymous.4open.science/r/beyond-coverage-code-3D5D.