Physical or visual realizations of higher-degree cohomological obstructions

Construct concrete physical or visual realizations of cohomological obstructions beyond degree two in the context of visual paradoxes, such as 2-gerbes classified by H^3, and provide explicit examples that demonstrate these higher-degree obstructions.

Background

The paper develops a cohomological hierarchy for bistable visual paradoxes, showing how ambiguity (H^0), conflict (relative H^1), impossibility (absolute H^1), curvature (relative H^2), and inaccessibility (absolute H^2) arise and can be detected using Z_2 coefficients and parity arguments. It identifies and illustrates phenomena up to H^2 in several systems (Necker cubes, gear meshes, rhombic tilings), including the discrete Stokes mechanism that promotes boundary obstructions to interior curvature.

In the conclusions, the authors note that while H^1 and H^2 have clear realizations in their framework, extending the hierarchy to higher degrees suggests considering gerbes and 2-gerbes. However, they explicitly state that physical or visual realizations of these higher-degree obstructions have not yet been found, marking this as an unresolved direction.