Schema Width Bounds the Benefit of Editable Keys for Plurality-Based Functional-Dependency Checks

A plurality-based functional-dependency check accepts a target's dependent value when it is the unique plurality among rows that agree with the target on a determinant. We study the minimum number of context-cell edits that makes every listed check accept a protected, initially rejected target, and ask how much cheaper this becomes when determinant (key) cells may change as well as dependent cells. For a family F of determinants sharing one dependent attribute, let w(F) be the size of a largest inclusion antichain among the determinants that contain a common key. We prove that the fixed-key optimum is at most w(F) times the editable-key optimum, and that every family has a binary table attaining exactly this factor. Hence the two optima agree on every such table if and only if F is laminar. With at least k+1 dependent values the factor is also attained at editable-key optimum k, whereas for a binary dependent attribute and two overlapping determinants the optima differ by at most one edit. The upper bound uses a margin-capped exchange that replaces each key edit by at most one dependent-cell flip per inclusion chain. The classification concerns the listed checks, not logical FD equivalence, and laminarity does not make optimization easy: acceptance within a budget remains NP-complete for singleton determinants. For the reverse direction we give an exact formula. Exhaustive finite checks of the main theorems cover 81,893 rejected table/family pairs. On Beers, Flights and Rayyan, all nine check families of our own earlier benchmark experiment are laminar, which explains, post hoc, why the accepting gain it predicted from editable keys could not occur.