  The determination of the specific angular momentum radial profile, $j(r)$, in
the early stages of star formation is crucial to constrain star and
circumstellar disk formation theories. The specific angular momentum is
directly related to the largest Keplerian disk possible, and it could constrain
the angular momentum removal mechanism. We determine $j(r)$ towards two Class 0
objects and a first hydrostatic core candidate in the Perseus cloud, which is
consistent across all three sources and well fit with a single power-law
relation between 800 and 10,000\,au:
$j_{fit}(r)=10^{-3.60\pm0.15}\left(r/\textrm{1,000au}\right)^{1.80\pm0.04}$ km
s$^{-1}$ pc. This power-law relation is in between solid body rotation
($\propto r^2$) and pure turbulence ($\propto r^{1.5}$). This strongly suggests
that even at 1,000\,au, the influence of the dense core's initial level of
turbulence or the connection between core and the molecular cloud is still
present. The specific angular momentum at 10,000\,au is $\approx3\times$ higher
than previously estimated, while at 1,000\,au it is lower by $2\times$. We do
not find a region of conserved specific angular momentum, although it could
still be present at a smaller radius. We estimate an upper limit to the largest
Keplerian disk radius of 60\,au, which is small but consistent with published
upper limits. Finally, these results suggest that more realistic initial
conditions for numerical simulations of disk formation are needed. Some
possible solutions include: a) use a larger simulation box to include some
level of driven turbulence or connection to the parental cloud, or b)
incorporate the observed $j(r)$ to setup the dense core kinematics initial
conditions.
