Dark-energy equation-of-state reconstruction (${\rho }_{\mathrm{de}}(z)={\rho }_{\mathrm{de},0}\exp [3{\int }_0^z(1+w)/(1+z^{\prime })d{z}^{\prime }]$)

energy conservation relates a separately conserved dark-energy density to its equation-of-state history. Distance measurements integrate the associated expansion history, making rapid variation difficult to recover uniquely. Growth and potential-evolution probes add information but depend on gravity and clustering assumptions. Consistency with $w=-1$ over a measured interval cannot prove that a field is exactly constant everywhere.