What does this equation mean?

Put the documentation and the independent benchmarks side by side and a pattern emerges that is more informative than any single score. Formalise the distinction the whole comparison rests on: let W be the context window a vendor documents for a given model, a fixed engineering figure set by attention implementation, position encoding, and what the serving stack supports. Let S(n) be some benchmark’s measured accuracy at input length n $\le$ W , and $S_0$ the same benchmark’s accuracy at a short reference length. For a chosen retention threshold $\tau$ , define the effective context length as $L_{\mathrm{eff}}(\tau) = \max\left\{\, n \le W \ :\ S(n) \ge \tau \cdot S_0 \,\right\}$. W is a documented constant, published on day one of a model’s release, identical no matter who asks. $L_{\mathrm{eff}}(\tau)$ is a measured variable — specific to a task, a threshold, a benchmark design, and a date — and every result surveyed above shows it running well below W well before W is reached. The two quantities answer different questions, and only one of them is available the moment a model ships.