LATHE writes seven crystallographic properties as differentiable objectives, enabling natural-language fine-grained crystal editing
The authors present LATHE, a geometric toolkit that expresses seven classes of crystallographic properties, namely bond length, bond angle, dihedral angle, coordination environment, lattice parameters, cell volume, and space group, as differentiable objectives so that a given crystal structure can be edited directly; on single-property benchmarks all seven property types reach near-perfect constraint satisfaction while optimized structures stay close to local energy minima, the LATHE-equipped agent translates over 87.5% of natural-language prompts into valid executable configurations, and in a band-gap inverse-design case study nine of ten independent runs reach the target tolerance window at a typical cost of thirteen hypothesis-evaluation cycles.