What does this equation mean?

A dataset-provenance audit built on this article’s transfer rate would ask it directly: before a model is retired, run its known distinctive traits against the descendant population it is suspected of having touched, and record $T_c$ alongside the shutdown date, the way a recall notice records which downstream products used a discontinued part. This would not resolve a dispute like the OpenAI-DeepSeek one after the fact, since by the time such a dispute becomes public the relevant training already happened outside anyone’s audit, which is exactly why Sacks could assert “substantial evidence” and OpenAI could decline to specify any of it without either side being checkable by an outsider [ 2 ] . It would instead change what a company can honestly claim going forward: that a specific quirk, once traced past a shut-down model’s retirement notice, either did or did not reappear in named descendants at a rate a sealed trial had already calibrated as meaningful, rather than remaining a plausible story either side is free to tell. Contractual bans on distillation, which several labs already write into their terms of service as a legal deterrent [ 3 ] , regulate a company’s stated intentions; a transfer-rate audit would regulate what its models actually left behind, which is a different and considerably harder thing to write around.