Bounded Agency: A Deployed Consumer-Health System in Which No Generative Model Computes a Number

A shopper reading an ingredient panel has seconds, one hand, and thirty chemical names in 6-point type, and that panel is also a primary allergen disclosure mechanism. The obvious agentic design, handing a multimodal model the photograph plus tools and a goal, fails for a reason easy to state and hard to engineer around: the quantities that decide the answer are the ones language models are least reliable at producing, and the user cannot check them. We describe a deployed mobile system built on the opposite principle. Generative models occupy exactly three roles, each bounded by the shape of its output space rather than by an instruction to behave: perception into a fixed JSON schema, entity resolution whose output space is $\mathcal{K}(t) \cup \{\varnothing\}$ so it may select but cannot invent an entity, and narration over values already fixed upstream. One invariant spans all three: a model may transcribe a number printed on a package, but no model may compute one. A transcribed value is falsifiable by the person holding the package; a derived value is not, so it belongs to deterministic code. Escalation to the generative adjudicator is gated on both confidence and dispersion, accepting $e^\star$ only if $P(e^\star \mid t) \ge \tau_P$ and $H(P(\cdot \mid t)) \le \tau_H$. We report deployment evidence from 791 scan records, 506 processed images with segmentation gates calibrated on 195 submitted photographs, and a 36-product in-aisle test, and we measure what grounding actually buys. Across 51 products for which we hold both our own photograph transcription and a populated public record, ingredient overlap averages 75.9%, yet the public record drops only 2 of 80 true (product, Big-9 allergen) pairs. Ingredient-level disagreement overstates allergen-level risk by roughly an order of magnitude, because major allergens are declared redundantly.