Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, transport cancellation, and crystalline reduction

Symmetric-cube hypergeometric coefficients at the mixed CM point (1/6, 1/3; 1) exhibit a clean arithmetic dichotomy governed by splitting in the Eisenstein decomposition of the logarithmic derivative. At split primes both Eisenstein pieces share the same local factor and the p⁴-tower survives; at inert primes a unit-root obstruction kills it. We prove by explicit counterexample that the natural bivariate congruence on the full Eisenstein module is false, while the congruence survives on the diagonal determined by the mixed combination Cₘix = C₀ − 27uC₀ — the unique Fricke-trace direction. A transport cancellation conjecture, verified through 144 exact rational-arithmetic tests for split primes p = 7, 13, 19, 31, reduces the nine low Cartier layers of the mixed defect to companion Vₚ-layers, which vanish by the companion theorem at (1/3, 1/3; 1). A staircase structure in the cancellation is identified: both Eisenstein components carry p-adic valuation exactly ℓ at layer ℓ, but their Fricke-trace combination gains an additional 4−ℓ powers of p, with the ℓ = 3 case being a mod-p statement on the special fiber. The order-2 recurrence has a MUM point at t = 1/108 with unit root αₚ = 1, and the conjectured exponent p⁴ exceeds the generic weight-3 Hodge-gap prediction of p³ (Roberts–Rodriguez-Villegas), reflecting a CM enhancement specific to split primes of the j = 0 curve. All unconditional results — order drop, modular dictionary, split/inert dichotomy, module-wide failure, and the conditional closure chain — are self-contained; the remaining gap is a unit-root identification in a descended rank-2 F-crystal on the Fricke quotient P¹ₜ.