THE SEMANTIC MANIFOLD: INNOVATION AS TOPOLOGICAL PROJECTION

Yaman, Tian, and Lindstr¨om (PNAS, 2026) demonstrate that human innovation does not
emerge from random combinatorial variation, but is strictly guided by “semantic knowledge”—
an internal cognitive map of conceptual relationships. We demonstrate that this cognitive
process is mathematically isomorphic to orthogonal projection onto a lower-dimensional
sparse invariant manifold. The unconstrained problem space corresponds to the dense, continuous state X. Semantic knowledge acts as the admissible manifold M. Innovation is
therefore the exact projection operation Ψ = Π(X). This finding rigorously validates the
KAN-DAM (Kolmogorov-Arnold Network - Dense Associative Memory) architecture of the
DSM-861 framework, proving that biological intelligence, much like hydrodynamic dissipation and chemical bonding, relies on rigid structural projection rather than continuous
stochastic search.