What does this equation mean?

Once a trait is defined, a population of models can be sorted by how they could plausibly have acquired it. Call a model vertically exposed if it shares a disclosed training relationship with the artifact’s source — a direct fine-tune of the source’s own weights, or a disclosed distillation run using the source’s outputs as training targets, the same mechanism named a decade ago as knowledge distillation, in which a smaller model is trained to match a larger one’s output distribution rather than raw labels [ 9 ] . Call a model horizontally exposed if it shares no weights or disclosed training relationship with the source at all, and its only plausible contact with the trait runs through an artifact the source produced — a dataset built from its outputs, a prompt template copied from its documentation, a piece of scaffold code encoding its behavior. Call a model unexposed , written $\varnothing$ , if no such channel, disclosed or suspected, connects it to the source. DeepSeek-R1’s later distillation into Qwen and Llama checkpoints, discussed below, is vertical by this definition, since the training relationship is disclosed and direct. DeepSeek V3’s self-identification is at best a candidate for horizontal exposure, since no training relationship between DeepSeek and OpenAI has been disclosed by either party — which is exactly why it is the harder case, and exactly why it needs a measurement rather than a press statement.