The distance-4 footprint of T and CCZ distillation without qubit recycling: 9 ≤ N_T(4) ≤ 10 and N_CCZ(4) = 10

In the model of Jacinto, Valcarce, Barizien, Gouzien and Sangouard (arXiv:2606.07734), a distillation protocol on N qubits is a sequence of Z-type π/8 Pauli-product rotations followed by check measurements, with no qubit recycling. Their quantity N_T(d) is the least N that supports an n-to-1 T-distillation protocol of distance at least d, for some n. They showed 8 ≤ N_T(4) ≤ 10; their SAT solver ran for two months on N = 8 without finishing. We show by an exhaustive computer search that no such protocol of distance at least 4 runs on N ≤ 8 qubits, for any n, so 9 ≤ N_T(4) ≤ 10. For n ≤ 54 this also follows from the classification of Wills, Jain and Singh; our search covers every n (after repeated columns are removed, n ≤ 127). We also confirm by an independent computation that no T-to-CCZ protocol of distance at least 4 runs on N ≤ 9 qubits, so N_CCZ(4) = 10. This bound was stated earlier, in other notation, in the public repository of Jain and Singh. At N = 8 a known reduction to Reed-Muller codewords leaves, up to symmetry, 12 × 2^29 linear systems over F2. Each was tested directly by one program and, through orbit representatives, by a second program written in a separate session. The proof is computer-assisted and has no formal certificate. This record holds the paper, its LaTeX source, and a zip with the code, outputs and logs.