空间几何与分析函数的联合推理要求将感知的空间配置转化为符号函数，其执行曲线需满足几何约束。我们提出 GAGR-Lab，一个通过笛卡尔游戏场景、显式函数语义及基于 Rust 的权威轨迹执行来测量该能力的框架。该框架区分了空间感知、度量基准化、几何关系、函数解释、函数构建及受约束合成。我们定义了四种可配置的场景难度预设和一种前瞻性的24格诊断设计，但仅报告实际评估的子集。一项针对单一托管模型（Llama 3.2 11B Vision Instruct）的有限试点研究使用两个 API 凭证作为执行副本，产生了72个平衡游戏、432次尝试、429个有效提供商响应，且无目标命中；探索性普通函数提示变体同样未命中，而结构化定位接口未产生可评分输出。特权分析搜索控制在来自300个生成场景的600个方向案例中独立成功，具有精确的可重复性，并通过了1,200次垂直反射或平移检查。该框架分离了服务可靠性、符号合规性和几何成功率，并保留了模型可见的精确输入和实现路径。分阶段协议概述了诊断校准、留出法复制、多模型比较及配对鲁棒性测试。贡献在于提供了一个包含已执行试点和明确前瞻性研究计划的操作型研究框架；完整的难度矩阵和对比模型结果尚未测试。

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 with 432 attempts, 429 valid provider responses, and no target hits; exploratory ordinary-function prompt variants also fail to hit, while the structured localization interface yields no scoreable outputs. A privileged analytic search control independently succeeds on 600 directional cases from 300 generated scenes, with exact repeatability and 1,200 successful vertical-reflection or translation checks. The framework separates serving reliability, symbolic compliance, and geometric success, and preserves exact model-visible inputs and realized paths. A staged protocol outlines diagnostic calibration, held-out replication, multi-model comparison, and paired robustness tests. The contribution is an operational research framework with an executed pilot and a clearly identified prospective study plan; the full difficulty matrix and comparative model results remain untested.