A numerical approach to model independently reconstruct $f(R)$ functions
  through cosmographic data
  The challenging issue of determining the correct $f(R)$ among several
possibilities is here revised by means of numerical reconstructions of the
modified Friedmann equations around the redshift interval $z\in[0,1]$.
Frequently, a severe degeneracy between $f(R)$ approaches occurs, since
different paradigms correctly explain present time dynamics. To set the initial
conditions on the $f(R)$ functions, we involve the use of the so called
cosmography of the Universe, i.e. the technique of fixing constraints on the
observable Universe by comparing expanded observables with current data. This
powerful approach is essentially model independent and correspondingly we got a
model independent reconstruction of $f(z)$ classes within the interval
$z\in[0,1]$. To allow the Hubble rate to evolve around $z\leq1$, we considered
three relevant frameworks of effective cosmological dynamics, i.e. the
$\Lambda$CDM model, the CPL parametrization and a polynomial approach to dark
energy. Finally cumbersome algebra permits to pass from $f(z)$ to $f(R)$ and
the general outcome of our work is the determination of a viable $f(R)$
function, that effectively describes the observed Universe dynamics.
