Dimension-free stability of binary-information contraction

Under the sharp contraction and joining results specified in the paper, we prove linear stability of binary-information contraction on every compact amplitude and correlation rectangle, uniformly over finite cube dimensions. For information psi(a) tending to zero, the constant grows at most as a to the power -4, and this exponent is necessary. The statements apply to arbitrary [-1,1]-valued kernels, without a mean restriction or a pointwise interior margin. We also strengthen the entropy-production inequality D(u) >= F(I(u)) by an absolute positive multiple of (E u) squared times I(u) squared. The proof combines strict Gaussian contraction, a compactness argument for joining laws, and estimates retaining the entropy of rare endpoint values.