What does this equation mean?

I have not measured $\phi_{\mathrm{sink}}$ for the checkpoints this paper actually tested, and no claim in this article depends on pretending otherwise. Doing so would require training matched softmax and sigmoid-attention models at Llama2 scale — a run measured in GPU-days this article does not have access to — and then rerunning Guo and Vosoughi’s own classification protocol on both. What can be stated precisely is the protocol and the threshold that would settle the question. Train the matched pair at each of the three Llama2 parameter counts the original paper tested — seven billion, thirteen billion, seventy billion — using the released sail-sg/Attention-Sink pipeline; reimplement Guo and Vosoughi’s own label-shuffling protocol on Banking77, GoEmotions, MASSIVE, TACRED, and RE-TACRED, unchanged; compute $\phi_{\mathrm{sink}}$ at each scale. A value clustering above roughly 0.7 across the size sweep would mean the sink accounts for most of what was measured, leaving little for “beyond mere engineering” to explain. A value clustering below roughly 0.2 would mean the sink is close to irrelevant to this particular effect, the hedge in the original sentence would be vindicated, and something the architectural account does not currently supply would be operating instead. Either outcome is worth knowing, and neither has been measured by anyone yet, including the authors of either paper this article draws on.