Bootstrap Dark Matter: Kuramoto Synchronisation on the Icosahedral Lattic

We derive the dark matter to baryon ratio from icosahedral lattice geometry and Kuramoto synchronisation theory. The theoretical maximum ratio decomposes as R_max = E/[D(D+1)/2] + χ/(D+2) = 30/6 + 2/5 = 27/5 = 5.400: the base vibrational-to-rigid mode ratio plus a topological correction from the Euler characteristic of the closed icosahedral surface distributed over its five-fold symmetry. The observed cosmic ratio (Planck 2018: 5.365) represents this maximum modulated by a coupling quality factor Q = r², the standard Kuramoto order parameter from nonlinear dynamics. We derive the coupling ratio K/K_c from first principles: the proton mass-energy sets the oscillator frequency (f_p = m_p c²/h = 2.27 × 10²³ Hz), the galactic gravitational potential sets the frequency spread (Δf/f ~ v²/c², gravitoelectric), and coherent disk rotation provides injection locking via the gravitomagnetic field with K/K_c = c/v ~ 1,500. This explains why all spirals achieve Q > 0.999, why the cosmic ratio is so precisely determined, and why galaxies without coherent rotation show reduced or absent dark matter signatures. A numerical simulation of 30 Kuramoto oscillators confirms the analytic predictions across five orders of magnitude in coupling strength. The framework applies established mathematics — Kuramoto (1975), Adler injection locking (1946), icosahedral mode counting — with zero free parameters. Six observational tests are proposed.