  We present the first interpretation of the Stokes profile asymmetries
measured in the FeI 630 nm lines by SOT/SP, in both quiet Sun internetwork (IN)
and network regions. The inversion is carried out under the hypothesis of
MISMA, where the unresolved structure is assumed to be optically thin. We
analyze a 29.52"x31.70" subfield carefully selected to be representative of the
properties of a 302"x162" quiet Sun field-of-view at disk center. The inversion
code is able to reproduce the observed asymmetries in a very satisfactory way.
The inversion code interprets 25% of inverted profiles as emerging from pixels
in which both positive and negative polarities coexist. kG field strengths are
found at the base of the photosphere in both network and IN; in the case of the
latter, both kG fields and hG fields are admixed. When considering the magnetic
properties at the mid photosphere most kG fields are gone, and the statistics
is dominated by hG fields. We constrain the magnetic field of only 4.5% of the
analyzed photosphere (and this percentage reduces to 1.3% when referred to all
pixels, including those with low polarization not analyzed). The rest of the
plasma is consistent with the presence of weak fields not contributing to the
detected polarization signals. The average flux densities derived in the full
subfield and in IN regions are higher than the ones derived from the same
dataset by Milne-Eddington inversion. The existence of large asymmetries in
SOT/SP polarization profiles is uncovered. These are not negligible in quiet
Sun data. The MISMA inversion code reproduces them in a satisfactory way, and
provides a statistical description of the magnetized IN and network which
partly differs and complements the results obtained so far. From this it
follows the importance of having a complete interpretation of the line profile
shapes.
