Cosmological fate from local expansion data (${\rho }_{m0}=(H_0^2-A_0)/(4\pi G),\Lambda c^2=H_0^2+2A_0$)

For a spatially flat universe consisting only of dust and constant cosmological constant, $A_0={\ddot{a}}_0/a_0$ and $H_0$ determine the two model parameters through the Friedmann equations. Predicting the future also assumes those matter laws persist. Local derivatives alone do not determine arbitrary future stress evolution: $a_{+}(t)=1+t+t^2/2$ and $a_{-}(t)=1+t+t^2/2-t^3$ agree through second derivative at zero, but the first expands forever and the second recollapses.