Extended TFT realization of graph coloring via 2-categorical bundles

Develop an extended topological field theory framework in which graph colorings are realized as sections of bundles defined at the level of 2-categories, as in the construction of bundles over 2-categories described in Construction cons:bundle_2-cat, thereby formalizing the coloring process as higher-categorical sections.

Background

The paper interprets local colorings as sections over basic-gons and sketches a higher-categorical notion of bundles and sections at the level of 2-categories. This suggests an extended TFT where objects, 1-morphisms, and 2-morphisms encode the local-to-global structure of colorings.

The conjecture calls for constructing such an extended TFT so that the coloring process matches 2-categorical sections, providing a conceptual foundation for the gluing rules used in the lattice TFT χ^{cw}.