Higher-dimensional nodal geometry and node inaccessibility

Develop the geometry of the osmotic divergence and the node-inaccessibility argument for higher-dimensional nodal sets of the two-state amplitude, where the nodal set is a codimension-two locus rather than a one-dimensional point or curve.

Background

The proved asymmetry between the bounded current part and divergent osmotic part of the weak momentum is fundamentally one-dimensional. In more than one spatial dimension, zeros of a generic complex two-state amplitude form codimension-two vortex-like sets, around which the phase winds and the current component can also diverge.

The paper explicitly leaves unresolved how the osmotic singularity and the stochastic inaccessibility analysis should be formulated in this higher-dimensional geometry.

References

In more than one dimension the nodal set becomes a codimension-two surface rather than a point, so $\partial\mathcal{D}$ is a higher-dimensional locus. The Madelung split and Theorem~\ref{thm:main} apply verbatim (Remark~\ref{rem:kinematic}), but the geometry of the osmotic divergence and the node-inaccessibility argument deserve separate treatment there (Remark~\ref{rem:scope}).

— Nodal obstruction to conditioned-diffusion representations of the weak momentum  (2609.03242 - Kam et al., 3 Sep 2026) in Conclusion; Remark Scope, Section Scope and limitations