Auditing Haldane Consistency in Reversible Enzyme Kinetics: A Curated Two-Sided Backbone and a Labeled Fold-Error Benchmark

Reversible enzyme kinetic constants can be audited through the Haldane relation: the apparent equilibrium constant implied by the rate law should match biochemical thermodynamics under matched conditions. We use the reciprocal cost $C_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{e}}=J(K_{\mathrm{e}\mathrm{q},\mathrm{k}\mathrm{i}\mathrm{n}}^{\mathrm{\prime }}\mathrm{/}{K}_{\mathrm{e}\mathrm{q},\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{o}}^{\mathrm{\prime }})$, with $J(x)=\frac{1}{2}(x+x^{-1})-1=\cosh (\ln x)-1$, as a calibrated, direction-symmetric reporting scale. The score is zero at agreement, penalizes reciprocal over- and underestimates equally, encodes the free-energy discrepancy in $RT$ units, and ranks records identically to $\mathrm{\mid }\mathrm{\Delta }\mathrm{\Delta }G\mathrm{\mid }$; the contribution is therefore biochemical curation, a reproducible workflow, and fold-error calibration rather than a new ordering. We apply the score to a curated demonstration set and, under prespecified inclusion criteria, assemble a two-sided backbone of twenty-one audited single-study records. Eight genuinely independent tests pair kinetics fit without a thermodynamic prior against separately measured equilibria; all eight fall within twofold (maximum $C_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{e}}=0.069$), although this remains a feasibility demonstration. Across the full backbone, eighteen records fall within twofold and three are flagged. The backbone is concentrated in carbohydrate isomerases and epimerases, so these results are within-family observations. Because real records carry no ground-truth labels, a semi-synthetic benchmark (twenty-nine within-twofold seeds, $\mathrm{1,885}$ injected known-error cases) quantifies detectability: AUC $0.784$ ($95\mathrm{\%}$ bootstrap CI $0.725$–$0.838$), conditional on the injected error taxonomy and invariant under monotone rescaling of $\mathrm{\mid }\ln x\mathrm{\mid }$. All data, code, protocol, and benchmark generator are archived for exact reproduction.