The $12\mathrm{C}(\alpha,\gamma)16\mathrm{O}$ rate at helium-burning energies to 10 percent
In plain words
When helium burns in a star, carbon-12 captures a helium nucleus to become oxygen-16 at a rate nobody has measured at the relevant energy. This one rate fixes the carbon-to-oxygen ratio of stars and the masses of the black holes they leave.
Precise statement
Determine the total astrophysical S-factor $S_{\mathrm{tot}}(E_{\mathrm{cm}}=300\,\mathrm{keV})$ of $\mathrm{12C}(\alpha,\gamma)\mathrm{16O}$ (E1 and E2 ground-state transitions plus cascades), at the Gamow peak for $T \sim 2e8\,\mathrm{K}$, with total uncertainty below 10 percent. Direct data stop near $E_{\mathrm{cm}} \sim 1\,\mathrm{MeV}$, so the answer requires either direct data closer to 300 keV or an R-matrix extrapolation whose subthreshold-state inputs (1- at 7.12 MeV and 2+ at 6.92 MeV in 16O) are fixed to the needed accuracy.
What would settle it
A direct measurement below $E_{\mathrm{cm}} \sim 0.8\ \mathrm{MeV}$ at an underground or high-intensity facility combined with a global $R$-matrix fit that reduces $S_{\mathrm{tot}}(300\ \mathrm{keV})$ to under 10 percent uncertainty.
Status in the literature
The 2017 R-matrix evaluation (deBoer et al.) remains the reference; no direct measurement has yet reached the Gamow window.