What does Tafel curvature measure? A signed composition law for electrochemical kinetics

Tafel curvature is often interpreted as a direct estimate of the reorganisation energy of an electrode reaction. This preprint examines the assumptions behind that interpretation using a decomposition of forward and backward rate constants into an affinity-dependent antisymmetric term and a time-symmetric kinetic term. Differentiating a network rate law yields a general chain-rule expression for apparent curvature in terms of step curvatures, degrees of rate control and their Hessian. For unit-stoichiometry consecutive steps, transfer-coefficient dispersion increases curvature; for parallel channels sharing an affinity, the corresponding variance decreases it. The resulting inequalities compare effective reorganisation energies with *weighted harmonic means* of local values, rather than necessarily with every individual step. The paper also analyses the effect of the metal-state continuum through the Marcus–Hush–Chidsey integral, including a local-exponential enhancement approximation with an explicit validity range, a finite-reorganisation-energy correction, and a vibronic model. A comparison of published results illustrates how estimates based on absolute rates and curvature can disagree; method and solvent differ simultaneously in that comparison, so it does not identify a method-specific bias. The central conclusion is that Tafel curvature constrains reorganisation energy only jointly with mechanistic, calibration and model assumptions. This Zenodo record contains the preprint PDF, the numerical reproducibility archive (Python scripts, regression tests, synthetic example and clearly labelled secondary transcriptions of published tables), and the LaTeX source archive. The numerical example recovers approximately 0.858 eV from synthetic data with 0.850 eV input under an explicitly *model-conditional* MHC inversion. No claim is made that the numerical code alone validates an absolute experimental reorganisation energy.