When Objectives Agree But Rules Do not: The Hidden Cost of Exposing Rule Errors In Optimization Models

An optimization-program revision may attain the expected optimum while enforc- ing the wrong rule, because the plans that expose the error can be worse than every operationally plausible decision. Such a revision passes any check that compares optimal objective values. We formalize this value–information barrier.The criti- cal loss ℓ(i, j) is the least objective degradation at which two rule interpretations disagree; its maximum against all alternatives exactly characterizes target identifia- bility from complete-plan membership answers. It also bounds the blind spot of objective-value checks. An LP slack law bounds exposure cost using rule slack and marginal value; a public-LP audit checks 63 constructed bound changes. A stored- data audit finds a strong association between the target’s own optimum loss and its critical loss (ρ =0.823 across 24,192 semantic classes). One post-hoc public complete-plan case has a model-derived 17.6% barrier; broad full-program LLM evidence remains unmeasured. Two sealed three-domain studies show a steep rise: 1.9–4.2% of update targets are identifiable using only optimal plans, compared with 64.7–67.8% at 10% loss. Factorial studies in two domains reproduce the frontier, and appended rules are harder to expose than retracted ones (67.8% versus 95.1% of classes at 10% loss). Critical-loss-Aware Planning (CAP) is an exact finite- budget reference that separates witness availability from question allocation and shows that isolating targets and shrinking ambiguity are different objectives. On 24 public benchmark revisions, 18/23 executable errors from three local models need positive local loss to expose. The evidence establishes a replicated finite-domain phenomenon and a limited public-task bridge; it does not estimate natural-history prevalence, open-ended generated-program loss, or human clarification cost.