Working Paper: Towards a Category-theoretic Comparative Framework for Artificial General Intelligence

Despite widespread discussion of AGI, there is no clear framework for measuring progress toward it. This ambiguity fuels subjective claims, makes it difficult to track progress, and risks hindering responsible governance. As a starting point to address this gap, we present a framework for understanding system capabilities in relation to human cognitive abilities. Drawing from decades of research in psychology, neuroscience, and cognitive science, we introduce a Cognitive Taxonomy that deconstructs general intelligence into 10 key cognitive faculties. We then propose a rigorous evaluation protocol in which a system's performance is measured across a suite of targeted, held-out cognitive tasks, generating a 'cognitive profile' that can be used to understand a system's strengths and weaknesses. We hope this framework will provide a practical roadmap and an initial step toward more rigorous, empirical evaluation of AGI.

General intelligence, of the kind that underwrites the full range of human cognitive achievement, is not a property of computational architecture alone. This paper advances a single thesis: the structural constraints on general intelligence occupy distinct levels of description and are mutually non-reducible, in the sense that the special-sciences tradition gives to that term. It follows that no single architectural advance, and no continuation of the scaling programme by itself, can produce artificial general intelligence (AGI), and that research programmes must be evaluated against the full constraint profile rather than against performance on any one benchmark. The thesis is developed through a method that reads general intelligence through four evidential lenses, AI systems research, anthropology, law, and economics, each anchored to a distinct level of description, supplemented by speculative fiction used as a disciplined heuristic in the context of discovery rather than the context of justification. Applying the method yields a taxonomy of twenty-three structural constraints organised into eight clusters; six are examined in depth and ordered as an ascending ladder of levels, with explicit bridges showing why progress at one level cannot carry to the next. The argument issues in five falsifiable predictions, each stated with a named benchmark family and a disconfirmation condition, converting a descriptive framework into a research programme with a longer horizon than the scaling hypothesis implies.

The agent harness, the system layer comprising prompts, tools, memory, and orchestration logic that surrounds the model, has emerged as the central engineering abstraction for LLMbased agents. Yet harness design remains ad hoc, with no formal theory governing composition, preservation of properties under compilation, or systematic comparison across frameworks. We show that the categorical Architecture triple (G, Know, Phi) from the ArchAgents framework provides exactly this formalization. The four pillars of agent externalization (Memory, Skills, Protocols, Harness Engineering) map onto the triple's components: Memory as coalgebraic state, Skills as operad-composed objects, Protocols as syntactic wiring G, and the full Harness as the Architecture itself. Structural guarantees-integrity gates, quality-based escalation, supported convergence checks-are Know-level certificates whose preservation is structural replay: our compiler checks identity and verifier replay, not output-layer correctness or model behavior. We validate this correspondence with a reference implementation featuring compiler functors targeting Swarms, DeerFlow, Ralph, Scion, and LangGraph: the four configuration compilers preserve three named certificate types by identity or replay, and LangGraph preserves the same certificates through its shared per-stage execution path. The LangGraph compiler creates one node per stage using the same per-stage method as the native runtime, providing LangGraph-native observability without reimplementing harness logic. An end-to-end escalation experiment with real LLM agents confirms that the quality-based escalation control path is model-parametric in this two-model, one-task experiment. The result positions categorical architecture as the formal theory behind harness engineering.