A minimal model of cognition based on oscillatory and current-based reinforcement processes

The paper correctly formulates the C5 model, derives the edge “complementarity” condition (either Dij*=0 or |Ni*−Nj*|=λ lij/q), and enumerates the three steady-state regimes E1, E2, and a both-paths-active regime that requires the two path lengths to be equal. It also shows non-hyperbolicity at the listed equilibria (e.g., zero columns in J at E1/E2). However, in the both-paths-active case, the paper specializes to the symmetric split with all five conductivities equal to aq/(2λ) and does not state the full one-parameter family of steady states D12=D23=α, D34=D45=D51=β with α,β≥0 and α+β=aq/λ, which exists whenever the two path lengths are equal. The candidate solution establishes precisely this family, and its Jacobian argument identifies the manifold’s tangent as a zero-eigenvector. Thus, beyond this omission, the logic and conclusions otherwise align. Key supporting points from the paper: model equations and complementarity (Eq. (8), Appendix A Eq. (15)–(22) ; E1/E2 values and N3*=a/b (e.g., Eqs. (24),(30); (33),(39) ); symmetric E3 with all D=aq/(2λ) and the necessary equal-path-length constraint l12+l23=l34+l45+l51 (Eqs. (53),(67) ); and non-hyperbolicity via Jacobians (zero columns at E1 and explicit JE3) .