Magic-state cultivation has so far focused mainly on single-qubit non-Clifford resources. We develop a direct cultivation architecture for the entangled state |CS⟩=CS|++⟩. Two commuting Clifford involutions project onto four usable branches related by Pauli-frame updates. A minimal six-bit [6,2,4] record protects the branch label against readout errors that map one valid record to another. Verified CAT₇ gadgets, Steane error detection, CZZ-based controlled checks, and immediate Steane-to-surface expansion form the complete factory. The decoder uses 263 operational detector bits, while 168 additional bits are withheld for later validation. Decoding proceeds through exact low-order resolution, a precomputed higher-order catalogue, and four-coset BP+OSD. Under the stated active-location stochastic-Pauli model, exact enumeration finds no accepted closed-boundary logical-failure mechanism through fault order two, while explicit order-three failure mechanisms exist. Finite-p simulations quantify acceptance, residual syndromes, and decoder workload, and targeted sampling of order-three faults estimates the leading logical-error channels. Optimizing the direct d=5→13 expansion reduces accepted-output operation count by approximately 35–37%. We compare the two routes at the same binary logical-error rate. Direct CS remains cheaper in operation count at the two lower-noise benchmark points even when the three-T route is given pre-existing output patches. The ordering reverses between 8×10⁻⁴ and 9×10⁻⁴. These results show that an entangled non-Clifford state can be cultivated directly with a protected branch record and an explicitly certified fault-order-three output channel.