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The Arnold-Bifurcation Dark Matter (ABDM) theory provides a non-particle solution to the 2026 Hubble and CMB anomalies. By deriving a 1.024 stability floor from Hamiltonian chaos, this framework reconciles local expansion at 72.93 km/s/Mpc and identifies the achromatic noise in IPTA DR3 as a metric property of a 7D Klein-bottle manifold.