We present spatially-resolved echelle spectroscopy of an intervening MgII-FeII-MgI absorption-line system detected at $z_{rm abs}=0.73379$ toward the giant gravitational arc PSZ1 G311.65-18.48. The absorbing gas is associated to an inclined disk-like star-forming galaxy, whose major axis is aligned with the two arc-segments reported here. We probe in absorption the galaxys extended disk continuously, at $approx 3$ kpc sampling, from its inner region out to $15times$ the optical radius. We detect strong ($W_0^{2796}>0.3$ r{A}) coherent absorption along $13$ independent positions at impact parameters $D=0$--$29$ kpc on one side of the galaxy, and no absorption at $D=28$--$57$ kpc on the opposite side (all de-lensed distances at $z_{rm abs}$). We show that: (1) the gas distribution is anisotropic; (2) $W_0^{2796}$, $W_0^{2600}$, $W_0^{2852}$, and the ratio $W_0^{2600}!/W_0^{2796}$, all anti-correlate with $D$; (3) the $W_0^{2796}$-$D$ relation is not cuspy and exhibits significantly less scatter than the quasar-absorber statistics; (4) the absorbing gas is co-rotating with the galaxy out to $D lesssim 20$ kpc, resembling a `flat rotation curve, but at $Dgtrsim 20$ kpc velocities decline below the expectations from a 3D disk-model extrapolated from the nebular [OII] emission. These signatures constitute unambiguous evidence for rotating extra-planar diffuse gas, possibly also undergoing enriched accretion at its edge. Arguably, we are witnessing some of the long-sought processes of the baryon cycle in a single distant galaxy expected to be representative of such phenomena.
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