Chentsov's Theorem

Non-existence of Information-Geometric Fermat Structures: Violation of Dual Lattice Consistency in Statistical Manifolds with $L^n$ Structure

Announce Type: replace Abstract: This paper reformulates Fermat's Last Theorem as an embedding problem of information-geometric structures. We reinterpret the Fermat equation as an $n$-th moment constraint, constructing a statistical manifold $\mathcal{M}_n$ of generalized normal distributions via the Maximum Entropy Principle. By Chentsov's Theorem, the natural metric is the Fisher information metric ($L^2$); however, the global structure is governed by the $L^n$ moment constraint.