Three controlled decay conditions can identify a generic linear drift with unknown fixed noise

We test when controlled state changes separate directed linear coupling from unknown correlated drive. We prove that two total decay conditions leave n(n-1)/2 local drift directions unresolved. Three conditions identify the drift and noise exactly if a matrix made from covariance differences has a simple spectrum. This condition holds generically for stable unrestricted drifts and positive definite fixed noise. A directed ring with independent noise remains ambiguous under any number of uniform decay changes. A fixed correlated input removes this ambiguity in the tested cases. In 15 identifiable synthetic models, exact recovery error was below 2e-10 of the recurrent-weight norm. Yet 0.1 percent covariance error gave median drift errors of 3.72 to 28.01 times that norm in the 32-node models. The results require full observation, known decay changes and noise that stays fixed. Freely changing correlated noise defeats local identification from any finite set of state covariances. No animal data were fitted. Code, proofs and all synthetic results are included.