Quantum Mechanics as Compact Phase Dynamics: Derivation from the Trit Axiom

We show that quantum mechanics — the Planck relation E = ħω, the de Broglie relation p = ħk, the Schrödinger equation, and the Born rule — are all consequences of a single equation: Cα^x c² = ħω, where x is the Trit winding number that determines particle mass through the formula m = Cα^x. The compact coordinate ϕ of every massive particle rotates at the Compton frequency ω = mc²/ħ, and the quantum mechanical wave function is the complex exponential of this phase: Ψ = e^{iϕ}. The electromagnetic wave is identified as the propagating zero-state of the Trit antisymmetric sector, carrying the photon phase ϕ_γ as its compact U(1) coordinate on S¹ ⊂ (S²)³. Phase conservation at the electromagnetic vertex, ϕ_γ = ϕ_{e,initial} − ϕ_{e,final}, is Maxwell's coupling derived from Trit geometry. Quantum randomness arises because the initial compact coordinate ϕ₀ is inaccessible at current energy scales (M_{LQ} = 1200 GeV); the Born rule is the marginal distribution obtained by averaging over ϕ₀. Quantum mechanics is not a fundamental theory: it is the ϕ₀-averaged dynamics of the Trit compact phase.