We show that the massless graviton equation ◻h_μν = 0, with exactly two physical polarisations, follows from two independent inputs: the non-commutativity [K̂_A, K̂_B] ≠ 0 of modular Hamiltonians of overlapping causal diamonds in a holographic CFT3, and the Ouroboros global consistency condition on kinematic data. No gravitational action is postulated.The derivation proceeds on the 6-dimensional kinematic space M_diamond = SO(3,2) / [SO(2,1) × SO(1,1)] of all causal diamonds in the 2+1-dimensional boundary. The modular non-commutativity is established by an exact Poisson bracket formula {k_A, k_B} = (4 / |a_A||a_B|) η^μν (x - c_A)_μ (x - c_B)_ν, valid for all diamonds (spherical and tilted), verified symbolically and numerically. Ouroboros global consistency is shown to be equivalent to John's integrability, placing kinematic data in the image of the spin-2 Radon transform R_2[h]. The Czech--John equivalence, extended to spin-2 by a new polarisation lemma, then gives (◻_KS - 2)F_ab = 0. Uniqueness of the solution follows from the D(3,2) doubleton representation of SO(3,2) (unitarity bound E_0 = s + 1 = 3, Casimir C_2 = 6) and the KMS boundary condition F(D_0) = δS(D_0) / 2π.Beyond the main theorem, three new results are established: (i) the exact bracket formula above, new to the kinematic-space literature; (ii) a polarisation lemma reducing spin-2 John's conditions to the scalar case algebraically; (iii) a no-go theorem showing that photon dynamics cannot arise from the same mechanism (C_2(D(2,1)) = 0 ≠ 6). A falsifiable prediction for TT-bar-deformed holography gives bulk graviton mass m² = ε(3 + ε) ≈ 3ε under E_0 → 3 + ε, connecting graviton mass directly to the Casimir eigenvalue of D(E_0, 2).