GAGR-Lab: Evaluating Joint Spatial-Geometric and Analytic Function Reasoning· GAGR-Lab: 评估联合推理能力

Joint spatial-geometric and analytic function reasoning requires translating a perceived spatial configuration into a symbolic function whose executed curve satisfies geometric constraints. We present GAGR-Lab, a framework for measuring this capability through Cartesian game scenes, explicit function semantics, and authoritative Rust trajectory execution. It distinguishes spatial perception, metric grounding, geometric relations, function interpretation, function construction, and constrained synthesis. We specify four configurable scene-difficulty presets and a prospective 24-cell diagnostic design, while reporting only the subset actually evaluated. A bounded pilot of one hosted model (Llama 3.2 11B Vision Instruct) using two API credentials as execution replicas yields 72 balanced games