A Primitive Theory of Next-Gen General Intelligence Based on Global Mathematical Verification Closed-Loop

Abstract

Existing Transformer and large model theoretical systems uniformly adopt the ”prediction-first” paradigm, defining intelligence as ”fitting the data distribution of the real world and next-token prediction”. This theory overturns conventional understanding and proposes the unique primitive of intelligence: a continuous, multi-layered, global closed-loop for mathematical verification and checking. All artificial intelligence behaviors (fitting, reasoning, association, generation, generalization, error correction, cognition) are essentially mathematical comparison, constraint checking, differential stability verification, and vector structure matching across different dimensions. All low-level operations of the traditional Transformer (vector embedding, QKV dot-product attention, gradient backpropagation, distribution fitting) are not ”predictive behaviors”, but native checking operations at the statistical level. The root causes of large model hallucinations, logical failures and generalization defects lie in the sole possession of statistical distribution checking, lacking rigorous mathematical checking of axiomatic structures, differential constraints and geometric topology. This theory constructs a ”dual-layer unified checking intelligence system”, completing a fundamental paradigm revolution from traditional probability-fitting intelligence to global mathematicalverification intelligence. It can directly guide the design of native intelligent models with no hallucinations, strong logic, self-correction capability and ontological cognition for the next generation.

Keywords