What does this equation mean?

Second, the meaning of a fixed number drifts, and quickly . Ho and colleagues, analysing more than two hundred language-model evaluations from 2012 to 2023, estimated that the compute required to reach a set performance threshold has halved roughly every eight months, with a 95% confidence interval of about five to fourteen months [ 19 ] . If a threshold is fixed at $C^{*}$ and efficiency improves with a halving time $\tau$ , the capability reachable below the threshold grows as though the budget were expanding: $C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}$. The analysis that follows is mine rather than the authors’. Taking the central estimate at face value, a threshold left unamended for two years admits models with roughly the effective capability that eight times the compute bought when the number was written; at the pessimistic end of the interval it is far more. The drift runs in both directions at once. Capable systems slip under the threshold as efficiency improves, while ordinary systems cross over it as hardware gets cheaper and larger training runs become routine. Under-inclusion and over-inclusion grow together, which is why the delegated-act power in Article 51 is not an afterthought but the load-bearing part of the design [ 4 ] .