Confounder or Mediator? Nuisance Probing Needs a Null Derived from the Design

Asking whether a representation encodes a nuisance variable while holding a variable of interest fixed is conditional effect estimation, and it inherits every requirement of one. Probing practice meets none: the conditioning set is hand-picked, overlap is never checked, the null is chosen for convenience, and effects are read against zero. The cost is not hypothetical. On a corpus built to contain no producer effect, naive probing declares one in 100% of trials and one-covariate-at-a-time conditioning still flags 43.1% of cells, where our procedure sits at 8.2% against a nominal 5% and still recovers a genuine direct effect in 61–63% of testable cells. The difficulty is that the controlled covariate is usually a mediator, not a confounder: an ENCODE lab chooses its measurement protocol ($\mathrm{U}(\text{protocol}\mid \text{lab})=0.349$ versus 0.097 given biosample), so conditioning on protocol blocks part of the effect being measured. We derive the conditioning set from the measured aliasing structure, report an identifiability budget as an overlap diagnostic (22 of 46 cells testable on ENCODE RNA-seq), permute within strata, and score against a nuisance-blind surrogate. On 759 ENCODE tracks this separates what neither alternative can: the producer effect is real under joint control (18 of 22 cells, balanced accuracy 0.994 against 0.402 chance), yet the model reproduces only the protocol-mediated component and essentially none of the direct one. The procedure retracted five of our own published-style claims along the way; we report them, because the pattern is the evidence.