The Inversion Error: AI System Design as Theory-Building and the Parametric AGI Framework: A Design Research Diagnosis of Structural Failures in Multimodal AI and a Formally Specifiable Solution Architecture

The current generation of Large Language Models has compressed the entire symbolic output of human civilization into a single synthesizable architecture — an unprecedented engine of consilience for human creativity and knowledge generation. What it has not accomplished — and what no amount of scaling will supply — is the structural foundation that makes symbolic cognition safe, coherent, and genuinely useful to users functioning within socio-technical systems overlaid on a physical world. This structural absence — the Inversion Error — is a failure of integration between the high-level symbolic reasoning of the Transformer and the foundational enactive constraints of the physical world. It manifests as three discrete, reproducible, and diagnosable failure modes: Continuity, Gravity and Physics, and Reversibility of Thought. These are not separate engineering problems. They are symptoms of one structural condition. The Parametric AGI framework proposes three formally specifiable, sparsely-gated Attention Mechanism modifications to the Transformer architecture — the Somatic Engine, the Gravity Engine, and the Episodic Buffer Engine — as the structural interventions that enforce the physical grounding the symbolic layer requires, addressing the structural gap between statistical pattern and physical constraint. Trained through Reinforcement Learning from Physical Feedback (RLPF) rather than human preference ratings, these engines address each failure mode respectively. The framework is grounded in abductive reasoning and AI system design understood as theory-building in Peter Naur's sense — a structural condition diagnosed from the socio-technical designer's vantage point, visible from outside the engineering system and invisible from within. This paper is simultaneously a diagnostic contribution, a solution architecture proposal, and a collaboration invitation to the mathematical, ML, and AI safety research communities.