Can multivariate Granger causality detect directed connectivity of a multistable and dynamic biological decision network model?

The paper empirically demonstrates, using MVGC/PWGC with sliding 100 ms windows, that (i) in the 420–520 ms stimulus-locked window INH↔U and forward INH→{L‑SM,R‑SM}, U→{L‑SM,R‑SM} are detected with stronger drive to L‑SM on correct and to R‑SM on error trials, and (ii) in the first 100 ms post-response, INH↔U, L‑M↔R‑M, INH/U→{L‑M,R‑M}, U→L‑SM, L‑SM→L‑M, and R‑SM→U are found, with correctness-contingent edges R‑SM→{L‑SM,R‑M} (correct) and INH→L‑SM (error); unifying these recovers most, but not all, of the original architecture and yields some spurious links . However, the paper stops short of a formal proof and explicitly notes missing connections and spurious ones, as well as using BY-FDR (not BH) for multiplicity control . The candidate solution correctly reproduces the specific edge lists and offers a plausible local-linear (Jacobian/TV‑VAR) rationale, but it overclaims 100% recovery of a target set and assumes BH-FDR and certain activation/lag conditions that the paper does not establish empirically; the paper itself reports only “most” recovery with some misses/spurious edges despite large samples . Hence both are incomplete: the paper is empirically sound but not a proof, and the model’s proof-style claims hinge on assumptions not verified in the paper and conflict with its stated limitations.