A property-registry contract for retrieve-or-refuse thermal-mechanical lattice search

Early thermal-mechanical lattice requirements are knowledge-intensive and often jointly unsatisfiable: an engineer asks for a cell that is light, stiff, laterally conducting and cheap, and no cell in the library satisfies it. A design system should say so, and say which requirement to loosen and by how much, rather than return the nearest row. A generative model can return a candidate even when the library holds none. This work applies established conflict diagnosis to a catalogue of homogenised properties. Search over 1,397 homogenised unit cells and 19 base materials (26,543 combinations) returns a catalogue row that a second solver can rebuild, or, for an empty feasible set of at most eight constraints, inclusion-minimal unsatisfiable subsets (MUS) and the slack of a repair, not a neighbour. One registry declaration generates the prompt and the evaluator, so undeclared parsed keys cannot reach search. On a frozen suite of 64 typed queries, retrieve-or-refuse matches min-repair on every feasible query (48/48) and refuses every empty one (16/16) with MUS and slack. Constraint-ignoring nearest-neighbour and penalty search violate stated cost or density limits. On 216 empty queries, repairs printed at three significant figures and rounded outward stay feasible in every case (216/216). When density and cost must be kept, a list of minimum-cardinality repairs keeps them on 209 of 211 queries; a protection-first repair keeps them on all 211, the same as full diagnosis. A 308-request parse benchmark is a template-text check, not unconstrained engineer prose.