Taming T-REX: A Canonical Language for Geometry-Aware Generative Design of Transition-Metal Complexes

String-based representations effectively handle organic chemistry but struggle with the topological complexity of transition-metal complexes (TMCs). We introduce Trans-pair Relations Expression (T-REX), a canonical notation that encodes coordination geometry via trans-pair maps. Validating T-REX on the previously published datasets reveals a stark geometric blind spot in experimental data: while our enumeration identifies over 20,000 additional accessible coordination isomers (expanding the topological space by ~200%), the original dataset contained only 72 resolved diastereomeric pairs. Beyond geometric enumeration, T-REX enables massive chemical space exploration through modular ligand substitution; applying this method to a seed set of 658 metal hydrides generates 2.3 million chemically plausible candidates. Finally, we demonstrate that hypergraph neural networks leveraging T-REX topology significantly outperform bond-based baselines on shape-sensitive properties like dipole moment (R² 0.71 vs. 0.52) without requiring 3D coordinates.