How are reconstructions stored?

the ea_reconstruction.mat file inside the patient directory stores the data (if you use lead group, the LEAD_groupanalysis.mat file stores a copy of all patient reconstructions).

There is a single variable reco inside the file that stores the data.

For instance,

reco.native.coords_mm{2}(3,:)

will be the left ({2}) third lowest ((3,:)) contact coordinates (in x, y, z order) in native postoperative (i.e. postop_tra.nii , postop_cor.nii, postop_sag.nii or rpostop_ct.nii) space. This space is similar to the preop space except for brainshift effects. If brainshift is minimal, coordinates could thus also be used in anat_*.nii spaces. However, if you did run brainshift correction, there will be a fourth entry called reco.scrf which will be in more precisely in anat_*.nii space.

reco.mni are coordinates in MNI space.

Similarly, reco.acpc is an automatic (Horn et al. 2017, also see this summary) transform to AC/PC space.