Four Points or Nothing: What a Batch Can and Cannot Measure at Its Own Leads

Campaigns in protein engineering and molecular design repeatedly ask a local question at the current best candidate: do these two changes interact here? We show that a batch can be full rank for the second-order interaction model and still contain no assumption-free measurement of a single one of the local interactions at its own leads: global identifiability does not imply local measurability. The estimand is the four-point contrast of a double-mutant cycle, so a model-free linear estimator of it, unbiased under every response function, exists if and only if all four points have been observed, and is then unique in that class. Auditing twelve batch rules on four real near-complete landscapes shows this is not an artefact of classical criteria: determinantal, gradient-embedding and redundancy-aware information batches reach the same near-zero certification as Bayesian $D$-optimality by three different routes, while naive exploitation certifies the most by accident. Three structural causes explain it, two computable from the proposed batch alone: separation to minimum Hamming distance two, occupancy below a classical extremal threshold, and rectangles away from the leads. An exact bias identity then gives a parameter-free boundary between direct measurement and the exact second-order projection, which a fitted model tracks but does not obey. It holds on 93 of 93 coordinate pairs, and a factorial sweep crossing it in both arguments puts the oracle crossing where the identity does.