A Unified Theory of Quantum Inertia and Entropic Gravity: Derivation of MOND from Vacuum Decoherence, Multi-Scale Tests, and Pre-Registered Euclid Predictions

We present a unified theory of quantum inertia and entropic gravity within the Entropy-Response Gravity (ERG) framework. The MOND interpolating function μ(x) = x/√(1+x²) is derived from the Unruh–de Sitter temperature via the fluctuation-dissipation theorem: inertia equals the directed (Unruh) fraction of the total (Unruh + Gibbons-Hawking) vacuum friction. The Holographic Zero-Source Principle is derived from the Rindler–de Sitter partition function, and cross-term corrections vanish exactly at the MOND transition (c₂(1) = 0). Multi-scale tests span 175 SPARC galaxy rotation curves (Simple wins 96/175), 242 ACCEPT clusters (12σ from null), the Bullet Cluster (entropy contrast 122±18%), 9,484 eRASS1 clusters (9.3σ M-T deviation), and a pre-registered Euclid DR1 prediction (η = 1.000 ± 0.01, testable October 2026)