Non-attainment of Jensen-Shannon SDPI Constants for Full-Support Channels

Jensen–Shannon SDPI constants of full-support channels are not attained by any fixed pair of inputs. Result. For binary-input channels with common output support, the Jensen–Shannon SDPI contraction coefficient ηJSD(W) is not attained by any fixed pair of input distributions. The ratio JSD(PW, QW)/JSD(P, Q) equals a weighted average of a strictly concave contraction function C(t), forcing strict inequality. The supremum is approached only by diagonal sequences, with convergence rate O(ε2). Using edge reduction (Ordentlich–Polyanskiy 2022), the result extends to all finite-input full-support channels. Addendum. Numerical examples (BSC, Z-channel, BEC), a convergence-rate theorem with proof, comparison with other divergences, an extended literature review (17 references) and reproducible Python code.