Geometric Criteria for Morrey Admissibility via the Real Log-Canonical Threshold

What the math gives to ML

The paper gives an explicit geometric criterion for local integrability of gradients of analytic singular kernels. This can be transferred to geometric attention or graph message passing by replacing generic relative-position biases with anisotropic singular kernels whose exponent is certified against an integrability budget. The transferable asset is the divisor-wise threshold p*(kappa), which can be sharper than the RLCT lower bound when the Jacobian vanishes along exceptional divisors. A practical experiment is to use a fixed quasi-homogeneous polynomial f of relative coordinates, constrain the learned singularity exponent, and test whether sharper locality improves geometric prediction without causing gradient explosions.