The KPZ universality class has multiple canonical fluctuation laws — Tracy-Widom distributions for point-to-point, point-to-line, half-space, and stationary geometries. Each has its own derivation. Each arises from its own boundary conditions.
Mu, Saberi, Moessner, and Kardar show that a single transfer-matrix product from a directed polymer in random media generates all of them. The different fluctuation laws emerge from different contractions of the same matrix product. Not different models. Not different random environments. Different projections of the same object.
The transfer matrix encodes the polymer's partition function as a product of random matrices, one per time step. The standard observable — the free energy — comes from tracking the matrix norm. But the same product contains other information. Contracting with different boundary vectors extracts different statistics: the GUE Tracy-Widom for flat initial conditions, the GOE for curved, the GSE for half-space, the Baik-Rains distribution for stationary.
The t^{1/3} scaling appears in all cases, confirming KPZ membership. But the matrix product also contains observables related to the leading eigenvalue that exhibit statistics outside the known Tracy-Widom classifications — new fluctuation laws hiding in the same mathematical object that generates the canonical ones.
The structural point: the different universality subclasses aren't different phenomena. They're different views of the same underlying random matrix product, selected by how you look at it. The universality lives in the product. The diversity lives in the projection.