Collapse Is Contraction: The Foss Interpretation of Quantum Mechanics

The measurement problem—the inconsistency between unitary evolution and irreversible collapse—has been open since 1927. We resolve it by identifying its structural origin. Using PS-Lifted dynamics (push-sum consensus on non-reversible lifted Markov chains with Z2 doubling), we test 21 quantum mechanical properties and classify each as HOLD or FAIL. Result: 12 of 21 properties hold (57%), 9 fail (43%). The separation is exact: a property holds if and only if it requires only linearity, topology, or contraction. It fails if and only if it requires unitarity or Hilbert space structure. The Birkhoff contraction coefficient τ = 0.508 is the order parameter: τ < 1 is the classical phase, τ = 1 is the quantum phase. The measurement problem dissolves because it presupposes unitarity. If evolution is contraction (τ < 1), both dynamics and measurement are irreversible—no contradiction, no paradox. Comparison with five interpretations of quantum mechanics shows the pilot wave (de Broglie–Bohm) as the closest classical analog: the physical projection is the particle, momentum is the guiding wave. The Foss Interpretation is: quantum mechanics is a unitary extension of classical consensus. The 57% that works is contraction and topology. The 43% that fails is the price of unitarity.