The Bradley Oscillation Field Theory: First‑Principles Derivation of the MOND Acceleration Scale (a₀ = cH₀ / 2π)

This paper presents a first‑principles derivation of the MOND acceleration scale within the Bradley Oscillation Theory scalar‑field framework. By evaluating the curvature‑coupled scalar action and its response to the FLRW background, I show that galactic dynamics undergo a freeze–thaw phase transition when local gravitational acceleration falls below the cosmic expansion threshold. This yields the exact identity a₀ = cH₀ / 2π ≈ 1.04 × 10⁻¹⁰ m/s², resolving MOND’s long‑standing theoretical gap. The derived acceleration scale naturally reproduces SPARC rotation curve flattening without dark matter and connects directly to BOT’s subatomic clock dampening and early‑universe acoustic horizon shrinkage. This publication establishes the cosmological origin of MOND behavior as an emergent scalar‑field boundary condition set by global expansion.