Bootstrap MOND: Deriving the Acceleration Scale from Icosahedral Mode Counting
Abstract
Modified Newtonian Dynamics (MOND) successfully reproduces galaxy rotation curves using a single empirical parameter, the acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s². Despite four decades of success, no theory derives this value from first principles or explains why MOND works at galaxy scale but fails at cluster scale. We derive a₀ = 5cH₀/27 from the Bootstrap Universe framework, matching observation to 1.0%. The denominator 27/5 is the same icosahedral mode ratio that sets the dark matter to baryon maximum (Keeble 2026): 30 vibrational modes over 6 rigid body modes, plus a topological correction from the Euler characteristic. The MOND acceleration scale is the cosmological acceleration cH₀ divided by the lattice coupling capacity — the threshold below which galactic gravity cannot maintain full Kuramoto synchronisation. This explains MOND's galaxy-scale success (single injection-locking driver, coupling quality Q ~ 1) and its cluster-scale failure (no single driver, variable Q). The dark matter halo 1/r profile is derived as the geometric consequence of 3D lattice propagation from a 1D rotation axis — the same structure as a line vortex in fluid dynamics. The Milky Way's Chakrabarti subhalo, located at an inter-arm shear zone, is identified as a sub-vortex in the coherence field. Five testable predictions are proposed.
Fields of Study & Subjects
Cosmology and Gravitation Theories
Pulsars and Gravitational Waves Research
Astronomy and Astrophysical Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 6 February 2026
- Document type
- Preprint