We use the recent results on solar acoustic modes coming from GOLF and MDI, to demonstrate that we improve the quality of the inversion of the sound speed and the density by avoiding several biases coming from the turbulent surface. The present accuracy allows a quantitative discussion on the physics of the solar nuclear core. We now exclude several phenomena which are incompatible with the present observations: central turbulent mixing or large modification of the pp chain nuclear reaction rates. We propose a solution to the difference between the Sun and solar models only in terms of turbulence at the base of the convective zone, an increase of the weak interaction p-p reaction rate by 2% in the framework of intermediate Mitler screening, and an underestimate of CNO composition of no more than 3%. Even if this solution is probably not unique, it allows a prediction of neutrino fluxes induced by helioseismology. We also note that nowadays, helioseismology puts just a few constraints on the reaction rates of the CNO cycle, and let place for lower high energy neutrino predictions.