clifford_eq_8
plain-language theorem explainer
The equality asserts that the single-qubit Clifford gate count in the recognition lattice equals eight. Quantum information researchers deriving gate sets from the J-functional equation would cite this when confirming the 2^D scaling for D equals three. The proof is a direct computational verification that the defining expression two to the power three evaluates to eight.
Claim. The cardinality of the single-qubit Clifford group equals eight: $|Cl_1| = 8$.
background
The module derives a natural gate set from the recognition lattice. Five canonical gates (H, X, Y, Z, CNOT) correspond to configDim D = 5, while the identity gate sits at J-cost zero. Single-qubit Clifford gates are the Pauli-phase combinations whose count is defined as two raised to the third power, matching the eight-tick octave period for D = 3. This rests on the upstream identity event at state one having zero cost and the equilibrium theorem that Jcost one equals zero.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate the arithmetic definition of cliffordSingleQubit as 2^3.
why it matters
This supplies the Clifford count required by the downstream gate certification qcGateCert, which packages the five canonical gates with the eight Clifford gates. It instantiates the eight-tick period (T7) and the emergence of three spatial dimensions (T8) inside the quantum-computing fragment of the framework. The result closes the counting step for the Clifford subgroup without introducing new hypotheses.
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