Why it is a question
THEORY-342 reports Jones’s exchange rate (LIT-1069, read in NOTE-884): on 9×9 Hex, at fixed Elo, about 15× less search for each 10× more training, down to a one-node search. It is one game, small boards, a modified AlphaZero with small fully connected networks, and no standard errors on the fitted coefficients. Whether the trade is a property of search against training in general, or of this implementation, is open.
What would answer it
The same iso-performance measurement (training compute against search compute at fixed strength) made on another game, or on Hex with a standard AlphaZero implementation or larger networks, with the slope reported with its uncertainty and the unit of test-time compute stated. A straight line in log–log space ending at a one-node floor would generalize the trade; a bending curve, or a slope that differs beyond the reported uncertainty, would confine it to Hex or to this implementation. More snapshots of the same 9×9 runs, or a refit of the same data in another functional form, cannot settle it.