Sharp Identification and Minimal Validation in a Two-Unit Encouragement Design

This paper studies population identification in a specified two-unit encouragement design with binary outcomes and partially validated treatment receipt. An exact finite response coupling preserves both units' joint outcomes in all four assignment arms and gives attained sharp endpoints for the controlled direct effect at zero actual peer exposure. For a known interior baseline compliance share, a validation design uniformly recovers the full-treatment sharp set if and only if it has positive support for focal validation in arm 10, peer validation in arm 01, and same-record joint validation in arm 11. Separate single-unit validations in arm 11 cannot replace joint validation. Observationally equivalent populations establish necessity, and the boundary compliance shares are treated separately. AI assistance was used for mathematical derivations, proof review, literature comparison, and manuscript preparation.