The Spatial Reasoning Gym: A Training Framework for Resolving World Model Class Failures in Multimodal AI

Current multimodal AI systems exhibit a reproducible architectural failure in physical grounding: a structural condition in which the Symbolic peak of cognition has been constructed without the Enactive base and Iconic middle that render symbolic output physically coherent. This condition, termed the Inversion Error 1, manifests as three formally specified failure modes: Continuity, Gravity, and Reversibility, and produces an aggregate diagnostic score of 4 out of 30 across three leading multimodal systems tested under the Spaghetti Table Protocol 1,2. The first paper in this series establishes the architectural diagnosis and proposes the Parametric AGI Framework: three formally specified attention mechanism modifications whose boundary conditions define the mathematical requirements for physical grounding at the level of the training architecture. The second paper proposes the interface-level governance response: a Chaos Monkey stress-testing methodology that positions human embodied cognition as a distributed diagnostic instrument. The present paper proposes the training environment, the Spatial Reasoning Gym, that generates the RLPF signal the Parametric AGI Framework's engines require to learn. The Gym is a procedurally generated, high-entropy three-dimensional physics environment in which a human designer, functioning as More Knowledgeable Other (MKO) in Vygotsky's sense 3, administers Reinforcement Learning from Physical Feedback (RLPF) 1 to scaffold the model's acquisition of physical grounding across a three-phase curriculum of escalating complexity. The MKO is not a preference rater in the manner of Reinforcement Learning from Human Feedback (RLHF) pipelines. Rather, the MKO functions as a Somatic Compiler 1: a structurally necessary participant in the training loop who supplies the physical ground truth, spatial constraint correction, and temporal reversibility guidance that the model cannot bootstrap from within its own architecture. The fitness landscape governing physical grounding training is rugged in Kauffman's NK sense 4: high interdependency among spatial, gravitational, and temporal constraints generates multiple local optima that gradient descent operating without global landscape guidance cannot reliably escape. This limitation holds even for modern adaptive optimizers when the interdependency structure of the fitness landscape is sufficiently dense. The MKO navigates this landscape in the direction of global physical coherence. This paper specifies the Gym's environment design, the MKO's operational role, the RLPF mechanism and its relationship to Proximal Policy Optimization (PPO), the three-phase Spatial Reasoning Gym Curriculum, two primary overfitting risks (social and environmental), and the institutional collaboration requirements for execution. The Gym is fully specified but not yet executed. It is presented here as a programmatic proposal and a collaboration invitation addressed to foundation model laboratories, XR research centers, and mathematical collaborators with the expertise to formalize the RLPF reward function.