Dimension\-Open Trace Witnesses Admit Exact Classical Memory Simulations

A common self-consistent channel diagnostic uses a reference contrast matrix R and a processed contrast matrix P. Under a fixed d-dimensional carrier, a common preparation/readout interface, and an invertible reference, one obtains W = Tr(P R^{-1}) = Tr T, where T is the transfer block on the d^2 − 1 traceless operator coordinates. Every entanglement-breaking d-dimensional channel obeys W ≤ d − 1. The inequality is useful only if the dimension and interface assumptions are part of the experimental contract. We construct an exact countermodel when they are not. For every d ≥ 2, set m = d^2 − 1 and let n_1, …, n_{m+1} be the vertices of a regular simplex in R^m. An affine encoding of a local m-dimensional signal ball into the m + 1 = d^2 classical simplex, paired with binary linear readouts, gives an invertible isotropic contrast matrix R = β I_m. The stochastic memory transition K_q = q I_{m+1} + (1 − q) 11^T/(m+1), 0 ≤ q ≤ 1, acts as r ↦ q r on the encoded local chart. Hence for every depth n the observed contrasts satisfy P_n = q^n R, all semigroup identities P_{n+k} = P_n R^{-1} P_k, and the apparent transfer spectrum is exactly that of the d-dimensional depolarizing channel. Yet the physical realization is a measure-and-prepare channel on a d^2-state classical memory and is therefore entanglement breaking for every q. A naive d-dimensional trace witness returns W = (d^2 − 1)q, which exceeds the legitimate entanglement-breaking threshold d − 1 whenever q > 1/(d + 1). At q = 1 the apparent violation factor is d + 1 although the physical memory is classical. Under affine mixture-preserving encodings, d^2 classical states are also minimal for faithfully representing an open (d^2 − 1)-dimensional interface chart. The result does not contradict valid dimension witnesses or trusted-input quantum-memory tests. It identifies a precise failure mode of transferring a dimension-conditioned trace certificate outside its interface contract: repetition consistency, spectral consistency, and arbitrarily deep Markov consistency do not by themselves recover the missing dimension assumption.