Derives ħ = m_p·c·r_p/(π·R₀) with 0.136% agreement (CODATA r_p) and 0.082% agreement (BFUT-derived r_p). Shows that the Compton wavelength hierarchy, de Broglie relation, uncertainty principle, harmonic oscillator ground state, tunnelling penetration depth, and all three Planck units follow from the same condensation geometry. Diagnoses the QFT vacuum energy discrepancy: the 10¹²¹ error arises from summing 17+ independent field modes and assigning ħω/2 to empty modes. One field at equilibrium gives ρ_vac = ρ_s·c² with no cancellation.