An Algebraic Decomposition of the MOND Acceleration Formula in Terms of the Matter-Dark Energy Equality Redshift

We show that the 1/6 exponent in the MOND acceleration formula a₀ = cH₀(Ω_Λ/Ω_m)^(1/6)/(2π) partially decomposes into standard cosmological physics: (Ω_Λ/Ω_m)^(1/6) = √(1+z_eq), where z_eq = 0.30 is the matter–dark energy equality redshift. The 1/3 comes from matter density dilution. The formula can be rewritten as a₀ = cH₀√(1+z_eq)/(2π). Of the two candidate cosmic transition epochs, only the equality epoch (z_eq = 0.30) produces an a₀ consistent with SPARC rotation-curve data; the deceleration epoch (z_accel = 0.64) is excluded at Δχ² ~ 1,290. Applied to galaxy clusters, the a₀ evolution correction reduces the MOND residual mass discrepancy by approximately 22%. This is an algebraic observation and empirical…