Preserve the Target, Relax the Sharpness: Certified Compression for Scalable Instrumental Variable Partial Identification

Sharp partial identification protects against false certainty, but exact causal representations can become large as outcome support grows. Naive coarsening reduces computation by changing the observed representation and can silently change the estimand or exclude data-compatible causal effects. We introduce a different computational primitive for finite instrumental-variable (IV) models: certified target-preserving stochastic representation reduction. A column-stochastic outcome map is lifted independently to every potential-outcome coordinate while treatment-response types are left unchanged. If the map preserves outcome values in expectation, observation commutes with the lift, every potential-outcome mean and affine mean contrast is preserved model-by-model, treatment-response restrictions are retained, and the original identified set is contained in the compressed set for arbitrary finite instrument and treatment cardinalities. Within the shared product-kernel class we characterize necessity and local uniqueness; with endpoint retention, nontrivial deterministic support reduction cannot satisfy the same exact mean-preservation certificate, so stochasticity is structural rather than cosmetic. We prove conditional sharpness bounds and a negative theorem excluding any support-uniform mesh-only rate, then turn nested support refinement into an anytime certified algorithm whose exact surrogate sets tighten monotonically to the original finite-support problem. A running-intersection rule preserves this monotonicity when the downstream causal optimizer is itself only outer-certified. Empirically, containment holds in all 13,660 generalized validation cells and all 7,692 nested refinement states. Adaptive allocation gives modest gains on nonadversarial cases and larger gains on an adversarial family, where observable-displacement-guided refinement reduces median width inflation at retained support size $M=32$ from 7.04% to 5.90%. Fresh-process one-thread timing shows representative multivalued-IV speedups of $8.0$–$18.7\times$, while an original outcome support of size $n=512$ compressed to $M=32$ gives a median $236\times$ speedup against the fastest certified exact backend. A nonasymptotic finite-sample extension and a public Job Training Partnership Act (JTPA) benchmark retain the same one-sided validity. We do not evade the exponential barrier for exact sharp analytical IV representations; we change the objective so that computation is traded against sharpness, not against the scientific target or validity.