Dense Associative Memory Is Not Neural: It Is a Many-Body Physical System

High-Order Polynomial Fields on Discrete Lattices, Exact Storage Capacities, and Combinatorial Regularization. The prevailing dogma of artificial intelligence asserts that machine cognition is achieved by increasingly precise imitation of biological brains or through continuous, unconstrained parameter fitting. We demonstrate that this paradigm conflates adaptive, lossy biological
heuristics with the formal preservation of logical structure. Dense Associative Memory (DAM) is not an algorithmic abstraction of a neural circuit; it is an exact, constrained many-body physical system operating on a discrete configuration space.