With equal white noise, fixed symmetric coupling can hide edge direction from FC in positive linear networks

We tested whether a small wiring gain after node similarity can bound causal coupling. For stable linear networks with fixed symmetric coupling and equal independent white noise, we prove that a skew direction change preserves the reference covariance exactly if and only if it commutes with the symmetric drift. A support-constrained nullspace test counts these changes. Positive rings with opposite one-way links have identical FC and all symmetric lag covariances, but different impulse responses. A 40-node example gives response 0.265 at one neighbour versus less than 1e-30 after reversal. Low-rank FC can coexist with this ambiguity. Unequal leaks remove exact ambiguity in the tested rings; small leak changes leave much smaller FC than response differences. Direction is available in the antisymmetric lag derivative under full unfiltered observation. This is a mathematical benchmark, not an animal-data result. The general covariance-preserving drift principle is established prior work. The result limits causal interpretations of FC prediction scores but does not change the empirical scores.