Can models store unlimited facts without growing larger?

Tool-augmented models are everywhere, but the theoretical case for why they help has been thin. This paper supplies it for factual recall. The number of facts a model can store purely in its weights is fundamentally bounded by its parameter count — so scaling knowledge capacity by enlarging the model is inherently inefficient. By contrast, a simple, efficient circuit construction proves that tool-use (external retrieval) enables unbounded factual recall without growing parameters.

The empirical half sharpens it into a phase transition: in-weight models need ever-larger architectures to memorize growing datasets, while tool-augmented models rapidly shift to rule-based querying once they observe enough diversity — decoupling memory capacity from model size. And the cost of the wrong choice is concrete: in-weight finetuning for factual recall degrades general capabilities, because limited capacity forces new facts to overwrite prior knowledge. Tool-based externalization preserves core skills, cuts training cost, and introduces minimal behavioral drift.

This gives a formal floor to the vault's harness thesis. Since Where does agent reliability actually come from?, in-tool learning is the provable version: externalize facts to tools rather than burning parameters and overwriting capability. It also predicts the failure mode behind Does repeated sensitive data in fine-tuning cause memorization? — finetuning facts in is exactly what memorizes and overwrites.