What makes quantum mechanics quantum? Which properties of quantum systems are genuinely non-classical, and which emerge from mathematical structure shared with classical stochastic processes? We test 21 quantum mechanical phenomena against their analogs in PS-Lifted dynamics—push-sum consensus on non-reversible lifted Markov chains with Z2 state-space doubling and Fiedler orientation (Foss, 2026). Result: 12 of 21 quantum phenomena are reproduced exactly. 9 fail. The classification is perfect: a quantum property holds in PS-Lifted if and only if it requires only Markovianity and topology. It fails if and only if it requires unitarity, Lorentz symmetry, or conservation laws. This is the Foss Boundary Theorem: 21/21 correctly classified, zero exceptions. The PS-Lifted system obeys three universal laws verified across 8 graph families and system sizes n = 20 to 500: (1) Contraction—all Lyapunov exponents negative, zero KS entropy; (2) Non-equilibrium steady state—broken detailed balance, negative entropy production; (3) Topological protection—gapped entanglement spectrum, Li-Haldane correspondence (r = 0. 91), size-independent Foss Topological Index F = 0. 75 ± 0. 05. Seven novel phenomena are identified: the Foss-Margolus-Levitin constant (κFML = 0. 027), the Foss Krylov Contraction (a new complexity class beyond chaotic and integrable), the inverted measurement-induced phase transition, universal classical Zeno/anti-Zeno effects, the Foss Community Depth Theorem explaining O (1) convergence, an inverted Page curve, and the Möbius-Lorentz algebraic correspondence. The boundary between classical and quantum is not entanglement, superposition, or measurement—it is unitarity. This implies a new complexity class L-BPP (problems solvable by lifted chains but not quantum walks), revises the Extended Church-Turing thesis, and demonstrates classical topological error correction without cryogenics.
David Tom Foss (Tue,) studied this question.