Classical Multipath Density Fails D3: A Constraint-Level Separation from Torus Spectral Structure

Lohmiller and Slotine (Proc. Royal Society A, 2026) show that classical constrained systems can reproduce quantum wave functions via multivalued action and density, establishing a computational equivalence between the Hamilton–Jacobi equation and the Schrödinger equation under appropriate density construction. This note evaluates that result against the D3 spectral discriminator (Tuckwell, 2026), which requires two independent commuting S1 actions and Z x Z winding-index organisation as the minimal algebraic condition for torus topology T2 = S1 x S1. The Lohmiller–Slotine construction does not satisfy the D3 condition: no independent cyclic generators, no commutativity requirement, and no Z x Z mode indexing…