Jensen–Shannon Contraction for Symmetric Channels: Exact Formula via Common-Component Reduction [Erratum: η_JSD = η_χ² for All m]

This work establishes exact strong data-processing (contraction) coefficients for the Jensen–Shannon divergence across symmetric discrete channels. A complete analytic proof shows that, for the binary symmetric channel, the JSD contraction coefficient is exactly \((1-2\delta)^2\), even though the generating function of JSD is not operator convex and standard equivalence theorems are therefore inapplicable. For all \(m\ge 3\) symmetric channels, we rigorously demonstrate a strict separation between the Jensen–Shannon and \(\chi^2\) contraction coefficients. This identifies the binary symmetric channel as the unique nontrivial symmetric channel family where these coefficients coincide for all noise levels. **ERRATUM (March 2026):** The exact formula η(W^(m)_δ) = λ²_m/s_m (Theorem 6) and its proof are correct. However, Corollary 7 is false: it claims η_JSD > η_χ² for m ≥ 3 by comparing with η_χ² = λ²_m, but λ²_m is the source-dependent (spectral) value. The common-component decomposition (Lemma 2) holds for ALL f-divergences, so the same derivation gives η_χ²(W^(m)) = λ²/s = η_JSD(W^(m)). There is no gap. The title claim "The Binary Case is Unique" is therefore incorrect.