  We present a formalism which allows for the perturbative derivation of the
Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and
observers. Entering the realm of small position uncertainties, we derive a
general asymptotic EUP. The leading 2nd order curvature induced correction is
proportional to the Ricci scalar, while the 4th order correction features the
0th order Cartan invariant Psi^2 (a scalar quadratic in curvature tensors) and
the curved space Laplacian of the Ricci scalar all of which are evaluated at
the expectation value of the position operator, i.e. the expected position when
performing a measurement. This result is first verified for previously derived
homogeneous space models and then applied to other non-trivial curvature
related effects such as inhomogeneities, rotation and an anisotropic stress
fluid leading to black hole "hair".
  Our main achievement combines the method we introduce with the Generalized
Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a
generic form of what we call the Asymptotic Generalized Extended Uncertainty
Principle (AGEUP).
