The AGI finite-determination conjecture for language-model entropy

Let $\mathcal{S}$ be the set of sentences, let $\mathscr{L}$ be a causal language model, and let

$$S_{\mathscr{L}}:\mathcal{S}\rightarrow\mathbb{R}$$

be its entropy function. The AGI finite-determination conjecture. If a causal language model is an Artificial General Intelligence, then there exists a finite subset $\mathcal{S}_{\mathrm{AGI}}\subset\mathcal{S}$ such that $S_{\mathscr{L}}$ on all of $\mathcal{S}$ is determined by its values on $\mathcal{S}_{\mathrm{AGI}}$. The motivation is the analogy with mathematics, where deductions from finitely many definitions and axioms determine further results; the paper gives no resolution of this conjecture.