  Understanding the observations of dynamical tracers and the trajectories of
lensed photons at galactic scales within the context of General Relativity
(GR), requires the introduction of a hypothetical dark matter dominant
component. The onset of these gravitational anomalies, where the Schwarzschild
solution no longer describes observations, closely corresponds to regions where
accelerations drop below the characteristic $a_{0}$ acceleration of MOND, which
occur at a well established mass-dependent radial distance, $R_{c}\propto
(GM/a_{0})^{1/2}$. At cosmological scales, inferred dynamics are also
inconsistent with GR and the observed distribution of mass. The current
accelerated expansion rate requires the introduction of a hypothetical dark
energy dominant component. We here show that for a Schwarzschild metric at
galactic scales, the scalar curvature, K, multiplied by $(r^{4}/M)$ at the
critical MOND transition radius, $r=R_{c}$, has an invariant value of
$\kappa_{B}=K(r^{4}/M)=28Ga_{0}/c^{4}$. Further, assuming this condition holds
for $r>R_{c}$, is consistent with the full spacetime which under GR corresponds
to a dominant isothermal dark matter halo, to within observational precision at
galactic level. For a FLRW metric, this same constant bounding curvature
condition yields for a spatially flat spacetime a cosmic expansion history
which agrees with the $\Lambda$CDM empirical fit for recent epochs, and which
similarly tends asymptotically to a de Sitter solution. Thus, a simple
covariant purely geometric condition identifies the low acceleration regime of
observed gravitational anomalies, and can be used to guide the development of {
extended} gravity theories at both galactic and cosmological scales.
