Classical pure-state cardinality conjecture

Let a classical physical system reproduce the statistical phenomenology of a generic physical statistical system, such as a quantum one. Its pure states are the states regarded as fundamental classical states, and in the quantum case the pure states form a manifold.

Classical pure-state cardinality conjecture. The set of pure states of the classical system cannot have lower cardinality than the set of pure states of the generic system. In the quantum case, the manifold of pure states of the classical system cannot have fewer dimensions than that of the quantum one.

The source notes that this is true for the classical models discussed there, including Bohmian mechanics and Nelson's models, whose additional variables increase the cardinality and are interpreted as physical fields. The conjecture is intended to express that particles alone cannot account for the phenomenology of Schrödinger's equation.