Split-prime supercongruences at a mixed CM point: unconditional mod p³ closure via Clausen convolution

We study symmetric-cube hypergeometric coefficients at the mixed CM point (1/6,1/3;1) on X₀(3). The full split-prime supercongruence A(mp) ≡ A(m) (mod p⁴) is reduced to a single scalar congruence A_pᵐⁱˣ ≡ 18 (mod p⁴). This scalar is evaluated unconditionally modulo p (Wolstenholme–Fermat–unit root), modulo p² (Eisenstein–Lerch endpoint theorem), and modulo p³ (Clausen convolution decomposition with Pfaff–Saalschütz evaluation and sixth-class harmonic matching). The mod p³ cancellation is exact: the endpoint term u_p and the middle correction W_p carry the same Θ_p digit with opposite signs. The remaining open level is mod p⁴.