We describe recent developments in the determination of the strong coupling from finite energy
sum rule (FESR) analyses of non-strange spectral distributions measured in hadronic 𝜏 decay,
focusing, in particular, on the consequences of a newly discovered redundancy in the “truncated
OPE” version of these analyses. Such analyses employ OPE fits to weighted spectral integrals
involving multiple weights at a single upper integration limit, $𝑠_0$ , with a number of the non-
perturbative contributions in principle present removed by hand. We show that (i) contrary to
conventional understanding, $\alpha_s$ in these analyses is obtained from fits which retain only perturbative
contributions to FESRs of a subset of spectral integrals involving weights of the highest (rather
than lowest) degrees entering the analysis, and (ii) the non-perturbative condensates nominally
determined in the full analysis are obtained in a redundant manner, leading to potentially very large
systematic uncertainties due to amplifications of any residual non-perturbative contamination of
the results for $\alpha_s$ produced by the perturbative tOPE truncation in the FESRs which determine
$\alpha_s$ . Finally, we show that alternate multi-weight, multi-$𝑠_0$ FESR analyses do not suffer from these
redundancy issues and, through their use of multiple $𝑠_0$ , provide non-trivial additional constraints
on the theory representations employed.

