Example. Counterexample: equal marginal reward, unequal prompt-local damage [ftip-00AS]
Example. Counterexample: equal marginal reward, unequal prompt-local damage [ftip-00AS]
Let two evaluation slices \(C_1,C_2\) have equal mass. A feedback channel returns an independent Bernoulli reward with mean \(1/2\) under either of two post-training protocols. Suppose their fixed-interface success changes are
\[ \left (\Delta _{\rm suc}(C_1),\Delta _{\rm suc}(C_2)\right ) =(-1,0) \quad \hbox {or}\quad \left (-\tfrac 12,-\tfrac 12\right ). \]
The reward law and its mean are identical, but the slice-level evaluation vectors differ. Hence marginal training reward does not determine whether damage is localized or distributed. This is a finite counterexample, not a claim about the mechanism in the source experiment.