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. 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 in 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. A structured pilot study, the Spaghetti Table Protocol, administered across three leading multimodal systems produces an aggregate score of 4 out of a possible 30 on a three-pillar diagnostic rubric, confirming the Inversion Error as a reproducible Class Failure of current transformer architectures rather than a model-specific artifact. 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. Trained through Reinforcement Learning from Physical Feedback (RLPF) rather than human preference ratings, these engines enforce the physical grounding the symbolic layer requires, addressing the structural gap between statistical pattern and physical constraint. 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 and ML research communities for formal engine specification, to the AI safety research community for corrigibility and inner alignment engagement, and to foundation model and world model development teams pursuing physical grounding for development-level access to active training environments. v2, April 2026. Revisions include: expanded theoretical framework (Wilson consilience framing, Friston free energy principle, extended mind thesis developed in full); new §3.2 on the design loop vs. engineering production cycle; empirical scoring corrected and methodologically justified (Pillar 3 excluded from collapse sequence condition, aggregate revised to 4/30 from 5/36); §4.5 retitled "Boundary Conditions for Mathematical Instantiation" added as transition to framework; section numbering corrected throughout (§4.5–4.7); expanded reference apparatus (29 to 40 references), including 40 Amodei/CRS citation for Pentagon-Anthropic dispute; Author Note substantially revised to specify original contributions and AI use explicitly; EBM/Neuro-symbolic paragraph added to Phase 2 Workstream 2.