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 test, not a first-principles derivation. The square root and the 2π remain underived. In plain language: For 42 years, the MOND acceleration scale — 1.2 × 10⁻¹⁰ m/s² — has been measured from galaxy rotation curves but never explained. We show it can be rewritten in terms of the matter–dark energy equality redshift, the epoch roughly 3 billion years ago when dark energy density overtook matter density. Tested against two candidate cosmic transitions across 175 galaxies, the data selects the equality epoch and rejects the deceleration epoch. Whether this correspondence reflects a physical connection or a numerical coincidence remains an open question.