Abstract.

We present a novel framework—termed Claraurence Theory—that resolves the Yang–Mills existence and mass gap problem through functorial correspondence between gauge theory and cognitive topology. The mass gap emerges as a topological spectral gap induced by genus reduction via the Faddeev–Popov ghost mechanism, reinterpreted as a puncture operator.

We establish that homoiconic transformations preserve relational structure while modifying representational form, thereby demonstrating that the Yang–Mills mass gap Δ > 0 is isomorphic to the genus-transition barrier in cognitive manifolds. This approach unifies computational complexity (P vs NP), gauge field theory, and topological algebra through categorical functors.