A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states

We give an explicit construction proving that the exact stabilizer rank of $m$ copies of the qubit face-center magic state is $O(2^{3m\mathrm{/}8})$. Two symmetry-related fifteen-term identities combine into a twenty-four-term decomposition at twelve copies. The balanced structure of this decomposition yields a substitution that adds eight copies at a cost of eight terms per existing term. The resulting bound ${\gamma }_T\le 3\mathrm{/}8$ improves the previously published exponent ${\log }_2(3)\mathrm{/}4$.